Hyperstructures in Chemical Hyperstructures of Redox Reactions with Three and Four Oxidation States

Fakhry Asad Agusfrianto, Sonea Andromeda, Mariam Hariri

Abstract


Hyperstructures find numerous applications across various disciplines. One notable application is in chemistry, particularly in the context of chemical reactions. In 2014, Davvaz introduced the concept of bi-hyperstructures, but their application specifically in chemical reactions, has yet to be thoroughly explored in previous studies. Thus, the primary aim of this paper is to examine and analyze the different types of bi-hyperstructures present within chemical hyperstructures. The scope of this study focuses on two types of chemical hyperstructures: redox reactions and reactions in electrochemical cells. Within these chemical hyperstructures, we investigate the possibility of bi-hyperstructures among bi-semihypergroups, bi-hypergroups, bi-H_v-semigroups, and bi-H_v-groups. Next, some properties of bi-hyperstructures related to hyperstructures are also investigate.


Keywords


Bi-Hyperstructures; Chemical Reactions; Hyperstructures; Hypergroups.

Full Text:

DOWNLOAD [PDF]

References


Agusfrianto, F. A., Hariri, M., & Mahatma, Y. (n.d.). Chemical Hyperstructures For Neptunium, Rubidium, and Plutonium. Journal of Indonesian Mathematical Society.(Submitted)

Al-Jinani, R., Al-Tahan, M., & Davvaz, B. (2019). Hypergroups and H_v-Groups Associated to Elements with Four Oxidation States. Facta Universitatis, 34(4), 689–708. https://doi.org/10.22190/FUMI1904689A

Al-Tahan, M. A., & Davvaz, B. (2018). Weak Chemical Hyperstructures Associated to Electrochemical Cells. Iranian Journal of Mathematical Chemistry, 9(1), 65–75. https://doi.org/10.22052/ijmc.2017.88790.1294

Al-Tahan, M., & Davvaz, B. (2019a). A New Relationship Between Intuitionistic Fuzzy Sets and Genetics. Journal of Classification, 36(3), 494–512. https://doi.org/10.1007/s00357-018-9276-8

Al-Tahan, M., & Davvaz, B. (2019b). Fuzzy Subsets of The Phenotypes of F_2 -Offspring. Facta Universitatis, 34(4), 709–727. https://doi.org/10.22190/FUMI1904709A

Al-Tahan, M., & Davvaz, B. (2022). Chemical Hyperstructures for Elements with Four Oxidation States. Iranian Journal of Mathematical Chemistry, 13(2), 85–97. https://doi.org/10.22052/IJMC.2022.246174.1615

Al Tahan, M., & Davvaz, B. (2017). Algebraic Hyperstructures Associated to Biological Inheritance. Mathematical Biosciences, 285, 112–118. https://doi.org/10.1016/j.mbs.2017.01.002

Chung, S.-C. (2019). Chemical Hyperstructures for Ozone Depletion. Journal of Chungcheong Mathematical Society, 32(4), 491–508. https://doi.org/10.14403/jcms.2020.33.4.469

Chung, S.-C., & Chun, K. . (2020). Chemical Hyperstructures For Stratospheric Ozone Depletion. Journal of Chungcheong Mathematical Society, 33(4), 469–487. https://doi.org/10.14403/jcms.2020.33.4.469

Chung, S. C., Chun, K. M., Kim, N. ., Jeong, S. Y., Sim, H., Lee, J., & Maeng, H. (2014). Chemical hyperalgebras for three consecutive oxidation states of elements. MATCH : Communications in Mathematics and in Computer Chemistry, 72(2), 389–402. https://match.pmf.kg.ac.rs/electronic_versions/Match72/n2/match72n2_389-402.pdf

Corsini, P., & Leoreanu-Fotea, V. (2003). Applications of Hyperstructures Theory. Kluwer Academic Publishers. https://link.springer.com/book/10.1007/978-1-4757-3714-1

Davvaz, B. (2016). Semihypergroup Theory. In Academic Press. https://doi.org/10.1007/978-3-658-15397-7_4

Davvaz, B., & Cristea, I. (2015). Fuzzy algebraic hyperstructures. In Studies in Fuzziness and Soft Computing (Vol. 321). https://doi.org/10.1007/978-3-319-14762-8

Davvaz, B., & Dehghan-Nezhad, A. (2013). Chemical Examples in Hypergroups. Ratio Matematica, 14(1), 71–74. http://arxiv.org/abs/1008.2438

Davvaz, B., Dehghan Nezhad, A., & Ardakani, M. M. (2014). Chemical Hyperalgebra : Redox Reaction. MATCH : Communications in Mathematics and in Computer Chemistry, 71, 55–63. https://match.pmf.kg.ac.rs/electronic_versions/Match71/n2/match71n2_323-331.pdf

Davvaz, B., Dehghan Nezhad, A., & Benvidi, A. (2012). Chemical Hyperalgebra: Dismutation Reactions. MATCH : Communications in Mathematics and in Computer Chemistry, 67(1), 55–63. https://match.pmf.kg.ac.rs/electronic_versions/Match67/n1/match67n1_55-63.pdf

Davvaz, B., & Leoreanu-Fotea, V. (2022). Hypergroup Theory. World Scientific. https://doi.org/10.1142/12645

Davvaz, B., Nezhad, A. D., & Heidari, M. M. (2013). Inheritance Examples of Algebraic Hyperstructures. Information Sciences, 224, 180–187. https://doi.org/10.1016/j.ins.2012.10.023

Davvaz, B., Nezhad, A. D., Mazloum-Ardakani, M., & Sheikh-Mohsenei, M. A. (2014). Describing the Algebraic Hyperstructure of All Element in Radiolytic Process in Cement Medium.pdf. MATCH : Communications in Mathematics and in Computer Chemistry, 72, 375–388. https://www.researchgate.net/publication/288809617_Describing_the_Algebraic_Hyperstructure_of_All_Elements_in_Radiolytic_Processes_in_Cement_Medium

Davvaz, B., & Vougiouklis, T. (2019). A Walk Through Weak Hyperstructures, A: Hv-structures. In World Scientific. https://doi.org/10.1142/11229

Douglas, B. E., McDaniel, D. H., & Alexander, J. J. (1992). Concepts and Models of Inorganic Chemistry. John Wiley & Sons, Inc. https://www.gbv.de/dms/ilmenau/toc/128985674.PDF

Heidari, D., Mazaheri, D., & Davvaz, B. (2019). Chemical Salt Reactions as Algebraic Hyperstructures. Iranian Journal of Mathematical Chemistry, 10(2), 93–102. https://doi.org/10.22052/ijmc.2018.114473.1339

Leoreanu-Fotea, V., Sonea, A., & Davvaz, B. (2023). The Fuzzy Degree of a Genetic Hypergroup. Annals of Fuzzy Mathematics and Informatics, 25(2), 125–138. http://www.afmi.or.kr/articles_in_%20press/2023-03/AFMI-H-221229R1/AFMI-H-221229R1.pdf

Marty, F. (1934). Sur une Generalization de la notion de groupe. Congress Math. Scandinaves, 45–49. https://www.semanticscholar.org/paper/Sur-une-generalization-de-la-notion-de-groupe-Marty/28b360e062f147b7a01e00713b40b46d948e00db

Nezhad, A. D., Moosavi Nejad, S. M., Nadjafikhah, M., & Davvaz, B. (2012). A physical example of algebraic hyperstructures: Leptons. Indian Journal of Physics, 86(11), 1027–1032. https://doi.org/10.1007/s12648-012-0151-x

Vougiouklis, T. (1994). Hyperstructures and Their Representation. Hardonic Press. https://hadronicpress.com/hyperstructures.pdf




DOI: https://doi.org/10.31764/jtam.v8i1.17011

Refbacks

  • There are currently no refbacks.


Copyright (c) 2024 Fakhry Asad Agusfrianto, Sonea Andromeda, Mariam Hariri

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

_______________________________________________

JTAM already indexing:

                     


_______________________________________________

 

Creative Commons License

JTAM (Jurnal Teori dan Aplikasi Matematika) 
is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License

______________________________________________

_______________________________________________

_______________________________________________ 

JTAM (Jurnal Teori dan Aplikasi Matematika) Editorial Office: