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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Jambura Journal of Biomathematics (JJBM) International Journal of Quantitative Research and Modeling
Asep K. Supriatna
Departemen Matematika, Universitas Padjadjaran
Computer Science & IT Decision Sciences, Operations Research & Management Engineering Environmental Science Mathematics Physics

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Characteristic of Quaternion Algebra Over Fields Faldiyan, Muhammad; Carnia, Ema; Supriatna, Asep K.
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 4 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v7i4.17625

Abstract

Quaternion is an extension of the complex number system. Quaternion are discovered by formulating 4 points in 4-dimensional vector space using the cross product between two standard vectors. Quaternion algebra over a field is a 4-dimensional vector space with bases  and the elements of the algebra are members of the field. Each element in quaternion algebra has an inverse, despite the fact that the ring is not commutative. Based on this, the purpose of this study is to obtain the characteristics of split quaternion algebra and determine how it interacts with central simple algebra. The research method used in this paper is literature study on quaternion algebra, field and central simple algebra. The results of this study establish the equivalence of split quaternion algebra as well as the theorem relating central simple algebra and quaternion algebra. The conclusion obtained from this study is that split quaternion algebra has five different characteristics and quaternion algebra is a central simple algebra with dimensions less than equal to four.
Application of Mathematical Model in Bioeconomic Analysis of Skipjack Fish in Pelabuhanratu, Sukabumi Regency, Jawa Barat Nurkasyifah, Fathimah Syifa; Supriatna, Asep K.; Napitupulu, Herlina
International Journal of Quantitative Research and Modeling Vol. 5 No. 1 (2024)
Publisher : Research Collaboration Community (RCC)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46336/ijqrm.v5i1.598

Abstract

Presently, sustainability has emerged as a crucial and compelling concern across diverse sectors, evolving into a long-term agenda championed by the United Nations through the implementation of the Sustainable Development Goals (SDGs). Within the SDGs, particularly under point 14 addressing life below water, emphasis is placed on ensuring sustainability in aquatic ecosystems, encompassing the fisheries sector. The concept of Maximum Sustainable Yield (MSY) holds significance in the bioeconomic analysis of fisheries, influencing decision-making processes aimed at preserving sustainability. Regrettably, several studies have identified inaccuracies in the determination of MSY, leading to instances of overfishing in various regions. Conversely, it is imperative to give due attention to Maximum Economic Yield (MEY) to ensure that economic considerations remain integral to decision-making processes. Consequently, a more comprehensive and detailed bioeconomic analysis, incorporating mathematical models, becomes essential. Among these models, the logistic growth rate model and the Gompertz growth rate model stand out as significant contributors. 
The dynamics of prisoner population model in Indonesia with a rehabilitation regulation for drug users to overcome prison overcapacity issue Triska, Anita; Dzulfikar, Muhammad Haekal; Supriatna, Asep K.
Jambura Journal of Biomathematics (JJBM) Volume 4, Issue 1: June 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjbm.v4i1.18898

Abstract

This paper discusses about a mathematical model of the prisoner population with a new regulation regarding punishments to the drug users in an effort to overcome the prison overcapacity issue in Indonesia. This new regulation is launched by the Indonesia government after a fact about overcapacity of prison in Indonesia is revealed through a fire incident in a prison on 8 September 2021 that causes 41 people died and a number of people were injured. Besides, prisons in Indonesia are mostly occupied by the drug user. The model is constructed by using a compartmental model approach. The stability analysis of the equilibrium points is carried out along with its existence conditions. The analytical studies are equipped by calculate the basic reproduction number. Furthermore, this study is also equipped by numerical simulations with some scenarios. The results of this study confirm that the effect of the new regulation is able to reduce overcrowded issue in prisons in Indonesia. However, if it compare to recent prison capacity, this new regulation has not been able to suppress the number of prisoner below to its capacity limit in the short time so that it is needed to consider other solutions as the additional regulation and policy
Co-Authors Anita Triska Dzulfikar, Muhammad Haekal Ema Carnia Faldiyan, Muhammad Herlina Napitupulu Nurkasyifah, Fathimah Syifa