Hyperstructures in Chemical Hyperstructures of Redox Reactions with Three and Four Oxidation States
DOI:
https://doi.org/10.31764/jtam.v8i1.17011Keywords:
Bi-Hyperstructures, Chemical Reactions, Hyperstructures, Hypergroups.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.
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
Downloads
Published
Issue
Section
License
Authors who publish articles in JTAM (Jurnal Teori dan Aplikasi Matematika) agree to the following terms:
- Authors retain copyright of the article and grant the journal right of first publication with the work simultaneously licensed under a CC-BY-SA or The Creative Commons Attribution–ShareAlike License.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).