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Jurnal Matematika Integratif
Published by Universitas Padjadjaran
ISSN : 14126184     EISSN : 25499033     DOI : http://doi.org/10.24198/jmi
Core Subject : Economy, Science, Engineering,
Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Electrical & Electronics Engineering Engineering Mechanical Engineering Transportation
Jurnal Matematika Integratif (JMI) is a national journal intended as a communication forum for mathematicians and other scientists from many practitioners who use mathematics in research. JMI received a manuscript in areas of study mathematics widely, and math-based multidisciplinary studies derived from outside problems of mathematics. All published articles in Jurnal Matematika Integratif are freely accessible in that website.
Arjuna Subject : Matematika - Matematika (Lain-Lain)
Articles 212 Documents
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Struktur Aljabar untuk Barisan Kodon dari Asam Deoksiribonukleat (DNA) Hasan, Nabila Nurmala; Kurniadi, Edi; Gusriani, Nurul
Jurnal Matematika Integratif Vol 21, No 2: Oktober 2025
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v21.n2.67778.213-228

Abstract

This article discusses the algebraic structure of codon sequences as a representation of DNA nitrogen base sets in mathematical terms. The study aims to prove what algebraic structures are obtained for codon sequences from DNA bases. The methods used include qualitative research methods in the form of literature studies and quantitative research methods in the form of experiments on DNA base sets. In mathematical notation, the nitrogen bases of DNA can be collected in a set and connected into algebraic structures through a bijective mapping on the Galois field of order 4. This results in the set B being viewed as a Galois field of order 4. Additionally, DNA base triplets or codons can be represented in mathematical form. Furthermore, these codons are bijectively mapped onto the Galois field of order 64, so that the resulting algebraic structure is a field. The result of this study show that the codon sequences have an algebraic structure in the form of a one-dimensional vector space over the Galois field on the codon. For further research, the Lie structure in codon can be investigated through the construction of its Lie brackets, where this vector space is a necessary condition for Lie algebras.
Analisis Dinamik pada Model Matematika Penyebaran Kekerasan Seksual dengan Pendekatan Rehabilitasi dewi, baiq indah rukmana; Nusantara, Toto; Hafiizh, Muchammad
Jurnal Matematika Integratif Vol 21, No 2: Oktober 2025
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v21.n2.66846.165-180

Abstract

Sexual violence is a serious issue occurring in various countries, necessitating special attention in its prevention and management. Mathematical modeling of sexual violence is crucial for understanding the dynamics of its spread and the impact of interventions on sexual violence cases. In this study, a four-dimensional nonlinear dynamic system model is used to analyze the stability of a sexual violence model considering the influence of rehabilitation. The basic reproduction number is calculated using the next-generation matrix method to estimate the potential spread of new cases caused by a single perpetrator in a vulnerable population. Analytically, there are two equilibrium points in the model: the sexual violence-free equilibrium point and the endemic sexual violence equilibrium point. Both equilibrium points are asymptotically stable, depending on the value of the basic reproduction number . The sexual violence-free equilibrium point is asymptotically stable under the condition , and the endemic sexual violence equilibrium point is asymptotically stable under the condition . Numerical simulations are conducted using the fourth-order Runge-Kutta method, implemented in MATLAB. The numerical simulation results also demonstrate that both equilibrium points exhibit the same stability properties based on the parameters used in this study.
Implementation of the Logistic Growth Model for Projecting the Population of Kuningan Regency in 2026–2035 Solihah, Aulia Zahratul; Sugandha, Agus; Puspita, Dian
Jurnal Matematika Integratif Vol 22, No 1: April 2026
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v22.n1.70221.133-144

Abstract

Differential equations are a branch of mathematics that are widely used to solve various problems in real life. In the context of population, differential equations are used to model and project the population in a region in a certain period. This Field Work Practice (PKL) Report aims to analyze population growth in Kuningan Regency using a logistic growth model and project the population in Kuningan Regency in 2025-2035. The data used is population data in Kuningan Regency in 2015-2024 obtained from the Kuningan Regency Central Statistics Agency. Based on the calculation results, nine logistic models were obtained with an environmental carrying capacity value of 1,266,373 people. Model VI was selected as the best model with a relative growth rate per year of 16.82% and a MAPE value of 1.34%. The model projects that the population of Kuningan Regency will continue to increase from 1,220,996 in 2025 to approximately 1,257,682 in 2035
Bi-derivation on Polynomial Ring Rinanda, Selvi Diana Dwi; Fitriani, Fitriani; Faisol, Ahmad
Jurnal Matematika Integratif Vol 22, No 1: April 2026
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v22.n1.70123.1-18

Abstract

Derivations and their generalizations play an important role in understanding the structure of rings. One natural extension of derivations is the notion of a biderivation, which is a bi-additive mapping satisfying derivation-type identities in each argument. In this paper, we investigate biderivations on polynomial rings. Several examples of biderivations are constructed and some of their fundamental properties are established. In particular, we study the relationship between biderivations defined on a ring $R$ and those induced on the polynomial ring $R[x]$. The obtained results provide additional insight into the behavior of biderivations under polynomial ring extensions.
Convolution One Dimensional Continuous Function on Fourier Series Expansion Gunawan, Gani; Respitawulan, Respitawulan; Fikri, Fariz Fahmi
Jurnal Matematika Integratif Vol 22, No 1: April 2026
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v22.n1.70224.83-90

Abstract

Convolution is an operation that involves two functions that can be used to transform a continuous input signal at every point in its domain so that a smooth output signal is produced at every point in the domain interval [1],[2]. But what happens when the convolution operation is applied to a function that is expanded through a Fourier series. The series is a series with a basis of differentiable functions, and how to perform convolutions that are expanded through the Fourier series. In this article, we will show a discussion to determine the product of the convolution function on the expansion of the Fourier series and the results obtained. Convolution One Dimensional ContinuousFunction on Fourier Series Expansion
Clustering Minimum Wages By Regency/City In Central Java Using The K-Means Clustering Method Nurrohman, Setia; Sugandha, Agus; Prabowo, Agung; Mashuri, Mashuri
Jurnal Matematika Integratif Vol 22, No 1: April 2026
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v22.n1.70220.19-36

Abstract

The Regency/City Minimum Wage (UMK) is an important indicator in describing the level of welfare and economic activity in a region. Central Java Province, which consists of 35 regencies/cities, has quite large variations in UMK between regions. This study aims to map the grouping of regencies/cities in Central Java based on the UMK level from 2021 to 2024. The analysis was conducted using the K-Means Clustering method with the help of Microsoft Excel and RStudio software through the stages of data standardization, the Kaiser Meyer Olkin test, determining the number of clusters using the Elbow method, and an iteration process to obtain optimal results. Based on the analysis results, it was obtained that the regencies/cities in Central Java can be divided into three clusters: cluster 1 consisting of 15 regions with a low UMK level, cluster 2 consisting of 14 regions with a medium UMK level, and cluster 3 consisting of 4 regions with a high UMK level. Most areas of Central Java are included in the low and medium UMK categories, while only a small number of regions are classified as having a high UMK. These results indicate the existence of welfare disparities between regions, so it is hoped that they can be a basis for the government in formulating policies to improve welfare and economic equality in Central Java Province. Keywords: Minimum Wage, Central Java, Disparitis, K-Means Clustering
Alternative Proofs for the Side Trisector Lengths Theorem of a Triangle Rahmayani, Indah; Mashadi, Mashadi; Gemawati, Sri
Jurnal Matematika Integratif Vol 22, No 1: April 2026
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v22.n1.70223.91-100

Abstract

In general, discussions regarding the line for side trisectors are still relatively limited compared to angle trisectors. For angle trisectors, most studies only discuss Morley’s Theorem and its extensions. Meanwhile, for side trisectors, existing papers usually calculate the lengths using both the sides and the angles of the triangle. A common problem is how to find the side trisectors length from its opposite vertex when only the side lengths are known. Furthermore, if the side trisector line is extended to form a tangential excircle, can we determine its radius. In this article, we discuss several alternative proofs to determine the lengths produced by side trisectors in a triangle. The main focus is to derive a formula for the side trisectors length using only the original side lengths and to find the radius of the tangential excircle. These proofs are done simply by using several geometric approaches, such as trigonometry, Stewart’s Theorem, and the Pythagorean Theorem. The result provide a standard formula for the trisector length, which is then used to find the radius of the tangential excircle in the constructed triangle
On the Structural Relationship Between the Characteristic and Minimal Polynomials of a Linear Operator Suharto, Istiqomah; Kurniadi, Edi; Carnia, Ema
Jurnal Matematika Integratif Vol 22, No 1: April 2026
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v22.n1.68420.37-58

Abstract

In this paper, we study the relationship between the characteristic and minimal polynomial of a linear operator, with a focus on figuring out under what conditions that the two polynomials equal each other. We emphasize that the characteristic and minimal polynomial of a linear operator are the same if and only if every eigenvalue has a geometric multiplicity of 1, which is equivalent to having only one Jordan block per eigenvalue. We provide an alternative proof for such a theory. For such matrices, we also show that the minimal polynomial can be easily derived from the normalized linear dependence of the Krylov sequence $\{v, Av, A^2v, \dots, A^{n-1}v\}$ for any generic vector $v$. We apply these algorithms to analyze the nilpotent and companion matrices. The results algorithmically verify that for a companion matrix $C$, its characteristic and minimal polynomials are identical and equal to its generating polynomial, $p_C(X)=m_C(X)=f(X)$. For a nilpotent matrix $N$ with index $k$, we confirm that its minimal polynomial is $m_N(X)=X^k$.
Application of Spatial Weight Matrix based on Semivariogram in Space-Time Autoregressive Integrative (STARI) Model for Financial System Forecasting in the Greater Bandung Region audina, yurid; Ruchjana, Budi Nurani; Abdullah, Atje Setiawan
Jurnal Matematika Integratif Vol 22, No 1: April 2026
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v22.n1.69207.101-118

Abstract

The global financial crisis of 2022 had a significant impact on the stability of Indonesia’s financial sector, marked by fiscal expansion and an increase in the money supply. The uneven distribution of liquidity across regions generated disparities in regional inflation, resulting in macroeconomic dynamics that exhibited a complex spatio-temporal structure. These conditions require a forecasting approach capable of capturing spatial and temporal interactions simultaneously. This study applies the Space Time Autoregressive Integrated (STARI) model to describe monthly inflation dynamics that are non-stationary due to inter-regional trends within Bandung Raya area. Spatial dependence is represented through spatial weight matrices constructed using three approaches matrices: uniform weights, inverse-distance weights, and isotropic semivariogram weights derived from population density data. Their effects on forecasting accuracy are compared using the Mean Squared Error (MSE). The novelty of the proposed approach lies in the use of an isotropic semivariogram as the basis for constructing spatial weights, allowing the model to capture continuous and heterogeneous spatial autocorrelation beyond traditional distance-based methods. Model parameters are estimated using Ordinary Least Squares (OLS) method implemented through Python scripts, and model evaluation is conducted using forecasting accuracy criteria and error diagnostics. The results indicate that the STARI(1,1,1) model incorporating semivariogram-based spatial weights outperforms both uniform and inverse-distance weights in terms of forecasting accuracy, because it has a minimum MSE. These findings provide valuable insights for economic policy formulation in Bandung Raya area.
Clustering of Banking Sector Stocks using Integration of Fourier Transform, Spectral Clustering, and Fuzzy C-Means as a Basis for Mean-Variance Portfolio Optimization Ricardo, Dimitri Salsabila Fakhriyah; Gusriani, Nurul; Napitupulu, Herlina
Jurnal Matematika Integratif Vol 22, No 1: April 2026
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v22.n1.69287.59-72

Abstract

The Indonesian capital market has experienced significant growth accompanied by high volatility, particularly in the banking sector whichholds a substantial contribution to market capitalization. Extremevolatility during the 2019-2024 period triggered by the impact of theCOVID-19 pandemic, economic recovery phases, and global macroeconomic challenges has created complexities in investment decisionmaking and portfolio optimization, which often produces unstable solutions under uncertain market conditions. Various studies have applied frequency domain analysis to uncover hidden patterns in stockprice movements or clustering to group stocks based on their characteristics to support optimal investment decision-making, however theintegration of these two approaches remains limited in its application togenerate robust portfolio optimization solutions in the Indonesian capital market. This study aims to generate clustering of banking sectorstocks through the integration of Fourier Transform, spectral clustering, and Fuzzy C-Means and to construct an optimal portfolio using theMean-Variance method based on the clustering results. This study usesclosing price data of 41 banking sector stocks on the Indonesia StockExchange for the 2019-2024 period through an integrated approach ofFourier Transform to extract frequency patterns, spectral clustering asa basis for grouping, Fuzzy C-Means to generate cluster membership degrees, and Mean-Variance for portfolio optimization. The results showthat the integration of these methods produces four optimal stock clusters consisting of nine stocks with a medium risk-low return profile,six stocks with a high risk-high return profile, fifteen stocks with a lowrisk-low return profile, and eleven stocks with a medium risk-high return profile. Based on the clustering results, four representative stockswere selected from each cluster for portfolio optimization, resulting inan optimal portfolio at a risk aversion value of ρ = 6.83 with a portfolio ratio of 3.4128877. This optimal portfolio is constructed from fourrepresentative stocks with weight allocations of 11.48% BMAS, 11.76%ARTO, 72.08% BNGA, and 4.68% BBHI, with an expected return valueof 0.0263613 and a portfolio variance of 0.0077241.

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