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Yuni Yulida
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Mathematics Department, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat University. Jl. A. Yani KM.35.8 Banjarbaru, Kalimantan Selatan
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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 226 Documents
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PEMODELAN MATEMATIKA PENYEBARAN PERILAKU PERUNDUNGAN DI SEKOLAH MENGGUNAKAN MODEL SBVR Titania Aulia; Bayu Prihandono; Nilamsari Kusumastuti
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 20, No 1 (2026)
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.v20i1.17735

Abstract

Bullying in the school environment is a social issue that adversely affects students’ psychological, social, and academic well-being. Understanding the dynamics of bullying behavior can be approached through mathematical modeling. This study develops a mathematical model of bullying behavior using the SBVR framework, which divides the population into four subpopulations: susceptible individuals, bullies, victims, and recovered individuals, to represent the dynamics of bullying behavior and evaluate the role of interventions in controlling it. The contribution of this study lies in the inclusion of a recovery compartment, which enables a more realistic representation of victim dynamics.The model is formulated as a system of nonlinear differential equations and analyzed to determine equilibrium points, compute the basic reproduction number as a key indicator of transmission potential, and evaluate the local stability of these equilibria. The results show that the model has two equilibrium points, namely a bullying-free equilibrium and a bullying-endemic equilibrium. The bullying-free equilibrium is locally asymptotically stable when the basic reproduction number is less than one, whereas the endemic equilibrium is stable when it exceeds one, indicating that this value acts as a threshold for the spread of bullying behavior. Numerical simulations show that increasing the effectiveness of interventions reduces the basic reproduction number and accelerates the decline in the number of bullies and victims. In addition, higher transition rates contribute to a faster spread of bullying behavior. These findings indicate that effective interventions play a crucial role in controlling bullying dynamics and can serve as a basis for developing strategies to reduce bullying in schools.
SIFAT INVARIAN TRANSLASI TOPOLOGI KONVERGENSI SERAGAM HAMPIR DIMANA-MANA PADA RUANG FUNGSI TERUKUR Haryadi - Haryadi; Solikhin - Solikhin
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 20, No 1 (2026)
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.v20i1.16747

Abstract

The space of functions that is often studied is the space of functions whose members are all measurable functions. One of the methods to study the space is by forming a topology. The problem is how to construct a topology on that function space. In this paper, a topology on the space of equivalent class of measurable functions will be constructed by building a local basis. The local basis of zero functions is used to define open sets in the space. This construction yields results that a topology can be constructed on the space. The resulting topology has the properties of being invariant under translation and being Hausdorff. Furthermore, convergence in that topological space is equivalent to almost everywhere uniform convergence.
MODEL SURVIVAL HIDUP PASIEN KANKER MATA MENGGUNAKAN METODE KAPLAN-MEIER DAN REGRESI COX PROPORTIONAL HAZARD Deyana Maulidya Rahmawan; Delia Nur Haliza; Samsul Arifin; Al Hujjah Asianingrum
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 20, No 1 (2026)
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.v20i1.18032

Abstract

Eye cancer is a relatively rare disease, but it can cause permanent vision impairment and even death if not treated properly. Differences in cancer type and patients’ clinical conditions are suspected to play a role in determining survival, so survival analysis is needed to describe survival patterns and identify factors affecting the risk of death. This study aims to analyze the survival of eye cancer patients and identify clinical factors influencing mortality risk using the Kaplan–Meier method and Cox Proportional Hazard regression. The research data were obtained from the Eye Cancer Patient Records dataset on the Kaggle platform, consisting of 5,000 medical records of eye cancer patients. Of these, 350 observations were used for Kaplan–Meier curve visualization so that survival patterns between groups could be more easily interpreted, while the Cox regression analysis was conducted using the prepared research data according to the modeling requirements. The results showed that cancer type was the only factor that significantly affected the risk of death. Patients with intraocular lymphoma had a hazard ratio of 1.54, meaning they had a 1.54 times higher risk of death compared to patients with retinoblastoma. Meanwhile, other variables such as gender, stage at first diagnosis, treatment type, surgery status, radiation therapy, and chemotherapy did not show a significant effect. Overall, these findings indicate that cancer type is the most prominent factor distinguishing survival between the two eye cancer groups analyzed.
KLASTERISASI GAYA BELAJAR MAHASISWA MATEMATIKA DENGAN FUZZY C-MEANS BERBASIS ATRIBUT VARK DAN HONEY-MUMFORD Didi Febrian; Hanna Dewi Marina Hutabarat; Philips Pasca G Siagian
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 20, No 1 (2026)
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.v20i1.17463

Abstract

Identifying student learning-style profiles is important for designing more adaptive instruction. However, prior studies on learning styles have mostly remained descriptive or correlational, while clustering-based mapping that integrates the VARK and Honey-Mumford models is still limited, particularly for Mathematics Study Program students. This study aimed to map student learning-style profiles using the Fuzzy C-Means (FCM) algorithm based on eight dimensions: Visual, Auditory, Read/Write, Kinesthetic, Activist, Reflector, Theorist, and Pragmatist. This study employed a descriptive quantitative approach involving 168 students of the Mathematics Study Program, FMIPA Universitas Negeri Medan. Data were collected through an online questionnaire; scores on the eight dimensions were averaged and combined as the input attributes for clustering. Cluster validity was evaluated using the Partition Coefficient (PC), Partition Entropy (PE), and Modified Partition Coefficient (MPC). The validity indices indicated that the two-cluster solution produced the best numerical values; however, the three-cluster solution was retained because it yielded more interpretable and less redundant profiles. For the three-cluster model, the values obtained were PC = 0.5222, PE = 0.8147, and MPC = 0.2834. The clustering results produced three profiles: Adaptive Multimodal (35.1%), Passive Kinesthetic (24.4%), and Practical Auditory (40.5%). These findings indicate that most students tend to learn more effectively through a combination of listening and direct practice.
MODEL DEEP LEARNING LSTM DAN GRU UNTUK PREDIKSI VALUTA ASING Santi Amalia; Oni Soesanto; Hermei Lissa
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 20, No 1 (2026)
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.v20i1.16263

Abstract

Currency exchange rates are one of the most important variables in macroeconomics because changes in exchange rates can affect economic stability and activity. The uncertainty of exchange rates is an important problem in finance, so accurate predictions are needed to design strategic steps in dealing with foreign exchange fluctuations. This research aims to explain the process of implementing the LSTM and GRU deep learning models in predicting foreign exchange against the Rupiah and US Dollar exchange rates and analyzing the evaluation results and prediction results of the LSTM and GRU models. The data used is the daily closing price of the USD/IDR exchange rate for the period August 29, 2014, to August 28, 2024, obtained from the global financial platform investing.com, totaling 2,554 data points. Predictions are made for a one-step forward horizon (t+1) with a chronological data division scheme of 80% as training data and 20% as testing data. Before the model training process, the data is normalized using the Z-score normalization method to improve data stability against outliers and aid the model learning process. The results showed that the LSTM and GRU models were able to learn historical data patterns well during the training and testing processes. During testing, the LSTM model produced an MAE of 0,133; RMSE of 0,159; and  of 0.932. After denormalization, the LSTM model has a mean prediction error (MAE) of approximately Rp65 and a RMSE of approximately Rp89 relative to the actual value. Meanwhile, the GRU model produced an MAE of 0.102; RMSE of 0.124; and  of 0.958. The denormalization results show that the GRU model has an average prediction error (MAE) of approximately Rp54 and an RMSE of approximately Rp70 relative to the actual value. The evaluation results show that the GRU model performs better than the LSTM model because it produces a smaller error value and the  value that is closest to 1.
ANALISIS RISIKO DAN RETURN SAHAM MENGGUNAKAN DOWNSIDE CAPITAL ASSET PRICING MODEL (DCAPM) PADA SAHAM IDX30 Hazwani Dhiya' Atiq Viatmaja; Hendra Perdana; Evy Sulistianingsih
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 20, No 1 (2026)
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.v20i1.18510

Abstract

The Indonesian capital market, as an emerging market is characterized by high volatility and an asymmetric return distribution, making the Capital Asset Pricing Model (CAPM) less representative for measuring stock risk and return. This study aims to analyze the relationship between risk and return of IDX30 stocks using the Downside Capital Asset Pricing Model (DCAPM), which focuses on measuring risk from the downside perspective through the estimation of downside beta. The data used consist of daily stock closing prices, the market index, and the risk free rate (BI Rate) from January 2023 to September 2025. A total of 20 stocks that consistently remained in the IDX30 index throughout the observation period were selected as the sample and grouped into portfolios based on their downside beta levels, which were subsequently evaluated using the Omega Ratio. Downside beta was estimated by dividing the asset semicovariance by the market semivariance. The results indicate considerable variation in downside risk among IDX30 stocks. From a financial perspective, a higher downside beta is associated with a higher expected return as compensation for greater downside risk. Moreover, portfolios with higher downside beta can still exhibit relatively good performance, provided that they generate returns exceeding the target return. These findings suggest that the DCAPM and Omega Ratio can serve as effective tools for evaluating stock portfolio risk and performance under asymmetric market conditions.

Page 23 of 23 | Total Record : 226

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