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. JURNAL MATEMATIKA INTEGRATIF HAS BEEN ACCREDITATED AS SINTA 3 SINCE VOL 14 NUMBER 1, 2018 BASED ON KEPUTUSAN MENTERI RISET DAN TEKNOLOGI/ BADAN RISET DAN INOVASI NASIONAL REPUBLIK INDONESIA NOMOR 200/M/KPT/2020 Journal Title: Jurnal Matematika Integratif Subject: Matematika Editor-in-chief: Dr. Sisilia Sylviani, M.Si Language: Indonesia, Inggris ISSN 1412-6184 EISSN 2549-9033 DOI: 10.24198/jmi OAI: http://jurnal.unpad.ac.id/oai/oai Frekuensi: 2 kali dalam satu tahun (April dan October) Published: Department of Matematics, FMIPA, Universitas Padjadjaran Acreditation: Sinta 3 Nomor: 200/M/KPT/2020 Published By: Department of Matematics, FMIPA, Universitas Padjadjaran Jl. Raya Bandung-Sumedang KM. 21 Jatinangor
Department of Matematics, Universitas Padjadjaran
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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.
Copyright (c) 2026 Selvi Diana Dwi Rinanda, Fitriani Fitriani, Ahmad Faisol https://creativecommons.org/licenses/by-nc-sa/4.0
Clustering Minimum Wages By Regency/City In Central Java Using The K-Means Clustering Method
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
Copyright (c) 2026 Setia Nurrohman, Agus Sugandha, Agung Prabowo, Mashuri Mashuri https://creativecommons.org/licenses/by-nc-sa/4.0
On the Structural Relationship Between the Characteristic and Minimal Polynomials of a Linear Operator
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 $m_N(X)=X^k$.
Copyright (c) 2026 Istiqomah Suharto, Edi Kurniadi, Ema Carnia https://creativecommons.org/licenses/by-nc-sa/4.0
Clustering of Banking Sector Stocks using Integration of Fourier Transform, Spectral Clustering, and Fuzzy C-Means as a Basis for Mean-Variance Portfolio Optimization
The Indonesian capital market has experienced significant growth accompanied by high volatility, particularly in the banking sector which holds a substantial contribution to market capitalization. Extreme volatility during the 2019-2024 period triggered by the impact of the COVID-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 stock price movements or clustering to group stocks based on their characteristics to support optimal investment decision-making, however the integration of these two approaches remains limited in its application to generate robust portfolio optimization solutions in the Indonesian capital market. This study aims to generate clustering of banking sector stocks through the integration of Fourier Transform, spectral clustering, and Fuzzy C-Means and to construct an optimal portfolio using the Mean-Variance method based on the clustering results. This study uses closing price data of 41 banking sector stocks on the Indonesia Stock Exchange for the 2019-2024 period through an integrated approach of Fourier Transform to extract frequency patterns, spectral clustering as a basis for grouping, Fuzzy C-Means to generate cluster membership degrees, and Mean-Variance for portfolio optimization. The results show that 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 low risk-low return profile, and eleven stocks with a medium risk-high return profile. Based on the clustering results, four representative stocks were selected from each cluster for portfolio optimization, resulting in an optimal portfolio at a risk aversion value of ρ = 6.83 with a portfolio ratio of 3.4128877. This optimal portfolio is constructed from four representative stocks with weight allocations of 11.48% BMAS, 11.76% ARTO, 72.08% BNGA, and 4.68% BBHI, with an expected return value of 0.0263613 and a portfolio variance of 0.0077241.
Copyright (c) 2026 Dimitri Salsabila Fakhriyah Ricardo, Nurul Gusriani, Herlina Napitupulu https://creativecommons.org/licenses/by-nc-sa/4.0
Alternative Proof of the Butterfly Theorem on a Hyperbola
The Butterfly Theorem originally applies to a circle. Several researchers have proven the Butterfly Theorem using various methods of proof. Furthermore, the theorem has been extended from its original application on circles to other conic sections, namely the parabola and the ellipse, also through different proof techniques. In addition, the development of the Butterfly Theorem can be applied to another conic section, the hyperbola, through an analytic approach. In this paper, the author proves the Butterfly Theorem on a hyperbola using Haruki’s Lemma. Haruki’s Lemma was originally established for circles. Therefore, the author develops Haruki’s Lemma specifically for the hyperbola, which is then used to prove the Butterfly Theorem on a hyperbola. Thus, a new proof of the Butterfly Theorem on a hyperbola can be established
Copyright (c) 2026 M. Teguh, Mashadi Mashadi https://creativecommons.org/licenses/by-nc-sa/4.0
Convolution One Dimensional Continuous Function on Fourier Series Expansion
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
Copyright (c) 2026 Gani Gunawan, Respitawulan Respitawulan, Fariz Fahmi Fikri https://creativecommons.org/licenses/by-nc-sa/4.0
Alternative Proofs for the Side Trisector Lengths Theorem of a Triangle
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
Copyright (c) 2026 Indah Rahmayani, Mashadi Mashadi, Sri Gemawati https://creativecommons.org/licenses/by-nc-sa/4.0
Application of Spatial Weight Matrix based on Semivariogram in Space-Time Autoregressive Integrative (STARI) Model for Financial System Forecasting in the Greater Bandung Region
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.
Copyright (c) 2026 yurid audina, Budi Nurani Ruchjana, Atje Setiawan Abdullah https://creativecommons.org/licenses/by-nc-sa/4.0
Green Economy-Based Multi-Objective Optimization Model for Agricultural Supply Chain Network Design Using Lexicographic Method
This Article presents a multi-objective optimization model for agricultural supply chain network design that incorporates green economy principles. The problem is formulated as a Many-to-Many Location Routing Problem (MMLRP) to address strategic decisions including Regional Food Hub site selection, commodity flow allocation between producers and hubs, distribution routing to consumer zones, and warehouse capacity planning. Two objective functions are solved hierarchically using the Lexicographic Method: maximizing demand fulfillment as the primary objective, followed by minimizing total costs comprising shipping, warehousing, and hub construction expenses. The model incorporates flow conservation constraints, capacity limits for producers and demand zones, and logical constraints linking distribution activities to hub establishment. Environmental considerations are integrated through carbon tax components and vehicle emission factors in transportation activities, enabling decision-makers to account for the environmental impact of logistics operations. Results demonstrate that the optimal network configuration identifies strategic hub locations and efficient distribution patterns characterized by short-distance delivery clusters that minimize carbon emissions, while maintaining cross-regional shipments from major production centers to satisfy demand requirements.
Copyright (c) 2026 Rizky Febrian, Diah Chaerani, Julita Nahar https://creativecommons.org/licenses/by-nc-sa/4.0
Implementation of the Logistic Growth Model for Projecting the Population of Kuningan Regency in 2026–2035
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
Copyright (c) 2026 Aulia Zahratul Solihah, Agus Sugandha, Dian Puspita https://creativecommons.org/licenses/by-nc-sa/4.0