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Yuni Yulida
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INDONESIA
Epsilon: Jurnal Matematika Murni dan Terapan
Published by Universitas Lambung Mangkurat
ISSN : 19784422     EISSN : 26567660     DOI : http://dx.doi.org/10.20527
Core Subject : Science, Engineering,
Decision Sciences, Operations Research & Management Transportation
Jurnal Matematika Murni dan Terapan Epsilon is a mathematics journal which is devoted to research articles from all fields of pure and applied mathematics including 1. Mathematical Analysis 2. Applied Mathematics 3. Algebra 4. Statistics 5. Computational Mathematics
Arjuna Subject : Matematika - Matematika Terapan
Articles 220 Documents
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PERBANDINGAN TIGA ALGORITMA PEWARNAAN GRAF DALAM MEWARNAI GAMBAR MOZAIK GEOMETRIS Santosa, Raden Gunawan; Tampubolon, Junius Karel
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 19, No 2 (2025)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v19i2.16712

Abstract

This study compares three graph coloring algorithms (Greedy, Welch–Powell (WP), and Marble–Matula–Isaacson (MMI)) applied to geometric mosaic images in the form of undirected graphs. Each vertex represents a region in the image, while edges connect neighboring regions. Two graphs are used as research objects, namely graph (a) with |V(GA)| = 56, |E(GA)| = 96, D(GA) = 0.062234, δ(GA) = 2, Δ(GA) = 7, and graph (b) with |V(GB)| = 55, |E(GB)| = 115, D(GB) = 0.0174, δ(GB) = 3, Δ(GB) = 6. The three algorithms are tested through 15 experiments to minimize the number of colors so that no two neighboring vertices have the same color. The Wilcoxon Rank-Sign statistical test shows that WP and MMI are significantly more efficient than Greedy, with p-values of 0.0006269 and 0.01073 (<0.05), respectively. The theoretical reason why the Greedy algorithm is not optimal compared to the other two algorithms is because the Greedy algorithm colors the vertices according to the input order without a vertex selection strategy based on degree or graph structure. These results confirm that WP and MMI are able to approach the theoretical limit of planar graph coloring as stated by the Four Color Theorem, which states that every planar graph can be colored with no more than four colors.
VARIABEL YANG MEMPENGARUHI KRIMINALITAS DI WILAYAH SULAWESI UTARA MENGGUNAKAN REGRESI DATA PANEL Rahmasari, Dwi Hartiana; Yulianto, Safaat
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 19, No 2 (2025)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v19i2.15377

Abstract

North Sulawesi Province has high economic and tourism potential due to its rich agricultural and mining resources and natural beauty, attracting investors and tourists. However, the high crime rate in North Sulawesi Province raises concerns about economic sustainability and social stability. Investors will tend to choose safe and stable places to invest, while tourists will also choose safe places to vacation. This study aims to analyze the variables that influence crime rates in North Sulawesi Province. Previous studies have shown that crime rates are influenced by several factors, including education, unemployment, poverty, and inequality. These variables will be analyzed using panel data regression. Panel data regression is used because crime rates vary across regions and over time. Thus, panel data can reveal the effects of inter-regional and inter-temporal factors. The study covers 11 districts and 4 cities in North Sulawesi Province, spanning the period from 2021 to 2023. The results of the panel data regression indicate that the most appropriate model is the Fixed Effect Model (FEM). Based on the results of the Fixed Effect Model (FEM), it is found that poverty and inequality significantly influence crime, while education and unemployment do not significantly influence crime. The Adjusted R Square value is 0.8132, meaning that 81.32% of crime in the North Sulawesi region can be explained by education, unemployment, poverty, and inequality, while 18.68% is explained by other factors.
NON-STANDARD SCHEME DISCRETIZATION (NSFD) FOR COMMENSALISM SYMBIOSIS MODEL WITH HARVESTING IN COMMENSAL POPULATIONS Puspitasari, Nurmaini; Faisal, Faisal; Yulida, Yuni; Jannah, Nur Wahidiyatil; Balya, Muhammad Afief
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 19, No 2 (2025)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v19i2.16551

Abstract

Dynamic analysis on the model of commensalism symbiosis with the discretized Michaelis-Menten cropping by using different schemes to non-standard finite difference (NSFD) is the main focus in this article. The analysis is started by searching the equilibrium points with their existence terms and local stability with their stability terms. In this article, there are four equilibrium points. The points are the extinction point of both populations, the host extinction point, the commensal extinction point, and the point where both populations can coexist (the coexistence equilibrium point). The existence of a host extinction point and a point at which both populations can coexist depends on the conditions of existence that must be met. Among the four equilibrium points, the commensal extinction point and the coexistence equilibrium point are locally asymptotically stable provided that the specified stability conditions are met. In the final analysis, numerical simulations were performed using the 4th order Runge–Kutta scheme for the continuous model and the NSFD scheme for the discrete model. The results show that the NSFD scheme offers greater flexibility in choosing the integration time step to ensure convergence to a feasible solution, outperforming the 4th order Runge–Kutta scheme in this respect.
ESTIMASI PARAMETER MODEL LOGISTIK DAN RICHARDS PADA PRODUKSI PADI: STUDI KASUS KALIMANTAN SELATAN Yulida, Yuni; Faisal, Faisal; Karim, Muhammad Ahsar; Hadi, Abdul; Wakhdah, Noorul; Amaliya, Tiara
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 19, No 2 (2025)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v19i2.16648

Abstract

Padi (Oryza sativa) merupakan komoditas pangan strategis di Indonesia karena beras menjadi sumber karbohidrat utama masyarakat dan berperan penting dalam menjaga ketahanan pangan nasional, termasuk di Kalimantan Selatan yang menjadi salah satu daerah produsen utama. Penelitian ini bertujuan mengestimasi parameter dan membandingkan kinerja model logistik dan Richards dalam memodelkan serta memproyeksikan produksi padi berdasarkan data historis dari Badan Pusat Statistik. Estimasi parameter dilakukan dengan metode nonlinear least squares, sedangkan akurasi model dievaluasi dengan Mean Absolute Percentage Error (MAPE). Hasil penelitian menunjukkan bahwa kedua model mampu merepresentasikan pola pertumbuhan sigmoidal produksi padi, dengan model Richards memberikan hasil yang lebih akurat (MAPE <15%) dibandingkan model logistik. Selain itu, analisis data luas panen mengindikasikan adanya penurunan signifikan sejak 2018, dengan kehilangan kumulatif sekitar 3,54 juta hektar pada periode 2003–2024 dan rata-rata penurunan tahunan sebesar 161 ribu hektar, yang diduga dipengaruhi alih fungsi lahan serta bencana banjir. Proyeksi skenario optimis menunjukkan adanya potensi peningkatan produksi, sedangkan skenario pesimis memperlihatkan kecenderungan stagnasi akibat keterbatasan lahan dan tekanan eksternal lainnya. Dengan demikian, model Richards dinilai lebih representatif dalam memproyeksikan produksi padi di Kalimantan Selatan, dan hasil penelitian ini dapat menjadi dasar dalam perumusan kebijakan perlindungan serta rehabilitasi lahan pertanian guna mendukung ketahanan pangan berkelanjutan.
ANALISIS KOMPARATIF METODE DES HOLT’S DAN ARIMA TERHADAP PERAMALAN TINGKAT PENGANGGURAN DI PROVINSI KALIMANTAN SELATAN Oktaviani, Yeni Rahma; Sa'adah, Yalela; Wibowo, Syahputra; Abdurrahman, Saman
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 19, No 2 (2025)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v19i2.17155

Abstract

Unemployment is crucial issue in South Kalimantan Province as it contribute to increased poverty and the slowing down of regional economic growth. Therefore, reliable forecasting method is needed to support the government in formulating strategic policies. This study aims to compare and identify a representative time series forecasting model for the TPT in South Kalimantan Province. This research compares the performance of the DES Holt 1-parameter, 2 parameter, and ARIMA (1,1,0) models using 19 years of semi-annual unemployment rate data (2005-2024). The models applied parameter optimization for  and , obtained by trial and error and by using R Studio, while accuracy was evaluated using MAPE. The research results show that the DES Holt-2parameter model with optimal parameters  and . Demonstrated better statistical performance compared to the DES Holt 1-parameter and ARIMA (1,1,0) models because it yielded the smallest MAPE error value of 4,66. However, the ARIMA (1,1,0) models is superior because it is more capable of capturing dynamic trend changes in the region, whether the changes are short-term of long-lasting, and can better reflect socioeconomic structural changes. The contribution of this research is to provide a scientific basis and a more superior and representative forecasting model, namely ARIMA (1,1,0), for the South Kalimantan Provincial government in formulating policies for job creation, improving labor productivity, and strengthening the regional economy in a sustainable manner.
PENERAPAN VECM DALAM MENGIDENTIFIKASI PENGARUH CURAH HUJAN DAN LUAS LAHAN TERHADAP PRODUKSI KOPI DI SUMATERA SELATAN Sangnandha, Habill Putra; Sulistijanti, Wellie
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 19, No 2 (2025)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v19i2.15392

Abstract

Coffee production in South Sumatra Province plays an important role in Indonesia’s economy, both as a source of foreign exchange and as a livelihood for farmers. During the 2020–2023 period, coffee production exhibited fluctuations that reflected instability and were suspected to be influenced by environmental factors such as rainfall and land area. This study aims to analyze the influence of rainfall and land area on coffee production using the Vector Error Correction Model (VECM), which is capable of examining both short-term and long-term relationships among cointegrated time series variables. The data used consist of monthly records of coffee production, land area, and rainfall obtained from the Central Bureau of Statistics for the 2020–2023 period. The analysis was conducted through a series of statistical tests, including stationarity testing, cointegration, determination of optimal lag, VECM estimation, Granger causality test, as well as impulse response function (IRF) and variance decomposition (VD). The results reveal the existence of a long-term relationship among the variables, where rainfall significantly affects coffee production, while land area does not show a meaningful effect. The VD analysis also emphasizes that rainfall’s contribution to production variation increases up to 10% in the long term, while the applied model is validated through the Portmanteau test. These findings confirm that climatic factors, particularly rainfall, play an essential role in maintaining the stability and sustainability of coffee production in South Sumatra.
PENDEKATAN MAZIMUM PENALIZED LIKELIHOOD UNTUK MENGESTIMASI FUNGSI BASELINE HAZARD PADA MODEL COX: STUDI KASUS PASIEN KANKER PAYUDARA Edina, Almira Ivah; Purnami, Santi Wulan; Sukur, Edi; Saputri, Prilyandari Dina; Febrisutisyanto, Ady; Alfajriyah, Aimmatul Ummah
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 19, No 2 (2025)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v19i2.17087

Abstract

Survival analysis is a statistical method that focuses on time-to-event variables, where the event time represents the duration a patient survives during the observation period. This study applies survival analysis to examine factors influencing the survival of breast cancer patients who are receiving treatment at C-Tech Labs Edwar Technology. The data used are right-censored survival data, referring to patients who either survived until the end of the observation period or died from unrelated causes. Risk factors analyzed include age, gender, and cancer stage, while treatment factors consist of surgery, chemotherapy, radiotherapy, and Frequency of Electro Capacitive Cancer Therapy (ECCT) usage. The Cox Proportional Hazard (PH) model combined with the Maximum Penalized Likelihood (MPL) method is used to analyze the effect of these factors on mortality risk, as well as to estimate regression coefficients and the baseline hazard function more accurately. The results indicate that age, frequency of ECCT use, and the status of additional therapies significantly affect patient survival. Older age increases the risk of death, while a higher frequency of ECCT use and the use of additional therapies help reduce that risk. Routine use of ECCT is shown to contribute to extending the survival time of breast cancer patients at C-Tech Labs Edwar Technology, Tangerang. However, potential confounding variables not examined in this study should be considered when interpreting the findings.
VALUE AT RISK VARIAN KOVARIAN PADA PORTOFOLIO OPTIMAL MULTI INDEX MODEL Putri, Mely Amara; Sulistianingsih, Evy; Imro'ah, Nurfitri
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 19, No 2 (2025)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v19i2.14924

Abstract

The construction of an optimal portfolio aims to minimize investment risk, with the Multi-Index Model being one method that accounts for multiple factors influencing stock returns. This study analyzes the optimal portfolio allocation and estimates potential losses using the variance-covariance Value at Risk (VaR) method. The study examines seven stocks from different sectors that have consistently been part of the IDX30 index from January 2019 to June 2024. The factors considered include the Jakarta Composite Index (JCI) and the exchange rate of the Indonesian Rupiah against the US Dollar (USD). The results indicate that the optimal portfolio consists of PT Adaro Energy Tbk. (ADRO), PT Bank Central Asia Tbk. (BBCA), and PT Kalbe Farma Tbk. (KLBF), with respective weights of 18.83%, 77.12%, and 4.05%. This portfolio yields a return of 1.22% with a risk level of 4.93%. The VaR calculation at a 95% confidence level indicates a maximum potential loss of 8.11% of the initial investment value.
PEMODELAN MATEMATIKA PENYEBARAN PENYAKIT DEMAM BERDARAH DENGUE DENGAN LARVASIDA SEBAGAI PARAMETER INTERVENSI Ekaristi, Mita; Prihandono, Bayu; Noviani, Evi
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 19, No 2 (2025)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v19i2.16718

Abstract

Dengue Hemorrhagic Fever (DHF) remains a public health threat in Indonesia. This study aims to analyze the effectiveness of larvicides in controlling DHF through a mathematical modeling approach. This study developed an SIR-ASI model that considers the aquatic phase of mosquitoes. The model was formulated as a system of nonlinear differential equations by integrating the parameter of larval mortality due to larvicides . The basic reproduction number  is derived using the Next Generation Matrix method. The stability of the system around the equilibrium point is analyzed using the Routh-Hurwitz criterion, which proves that the disease-free equilibrium point is locally asymptotically stable when . Numerical simulations indicate that increasing larvicide intensity  significantly reduces  from 3.19051 (without intervention) to 0.68281 (with intervention), equivalent to a 78.60% reduction. Sensitivity analysis identified u as one of the key parameters controlling  along with mosquito bite frequency  and mosquito mortality . The results of this study prove that larvicide intervention is effective in breaking the DHF transmission cycle by suppressing the vector population, thus making it a consideration in vector control strategies
LOWER LEVEL SUBGRUPOID Abdurrahman, Saman; Hijriati, Na'imah; Thresye, Thresye; Idris, Moch; Lestia, Aprida Siska
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 19, No 2 (2025)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v19i2.15332

Abstract

This study investigates the structure of anti-fuzzy subgroupoids within the framework of groupoids, extending the theory of fuzzy subgroups beyond traditional group-based algebraic systems. While numerous fuzzy approaches have been applied to groups and semigroups, the exploration of groupoids algebraic structures without the necessity of identity or inverse elements remains limited, particularly in the context of anti-fuzzy theory. This research addresses that gap by developing a mathematical characterization of anti-fuzzy subgroupoids and systematically analyzing their relationship with lower-level subsets. A key result demonstrates that every subgroupoid can be represented as a lower-level subset of a suitably constructed anti-fuzzy subgroupoid. Furthermore, it is shown that equality of two lower-level subsets occurs if and only if no element exists with a membership value strictly between the corresponding thresholds. Employing a deductive and axiomatic approach, this work contributes to the theoretical advancement of fuzzy structures in non-classical algebra. It offers a foundation for future applications in uncertainty-based decision systems

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