BAREKENG: Jurnal Ilmu Matematika dan Terapan
BAREKENG: Jurnal ilmu Matematika dan Terapan is one of the scientific publication media, which publish the article related to the result of research or study in the field of Pure Mathematics and Applied Mathematics. Focus and scope of BAREKENG: Jurnal ilmu Matematika dan Terapan, as follows: - Pure Mathematics (analysis, algebra & number theory), - Applied Mathematics (Fuzzy, Artificial Neural Network, Mathematics Modeling & Simulation, Control & Optimization, Ethno-mathematics, etc.), - Statistics, - Actuarial Science, - Logic, - Geometry & Topology, - Numerical Analysis, - Mathematic Computation and - Mathematics Education. The meaning word of "BAREKENG" is one of the words from Moluccas language which means "Counting" or "Calculating". Counting is one of the main and fundamental activities in the field of Mathematics. Therefore we tried to promote the word "Barekeng" as the name of our scientific journal also to promote the culture of the Maluku Area. BAREKENG: Jurnal ilmu Matematika dan Terapan is published four (4) times a year in March, June, September and December, since 2020 and each issue consists of 15 articles. The first published since 2007 in printed version (p-ISSN: 1978-7227) and then in 2018 BAREKENG journal has published in online version (e-ISSN: 2615-3017) on website: (https://ojs3.unpatti.ac.id/index.php/barekeng/). This journal system is currently using OJS3.1.1.4 from PKP. BAREKENG: Jurnal ilmu Matematika dan Terapan has been nationally accredited at Level 3 (SINTA 3) since December 2018, based on the Direktur Jenderal Penguatan Riset dan Pengembangan, Kementerian Riset, Teknologi, dan Pendidikan Tinggi, Republik Indonesia, with Decree No. : 34 / E / KPT / 2018. In 2019, BAREKENG: Jurnal ilmu Matematika dan Terapan has been re-accredited by Direktur Jenderal Penguatan Riset dan Pengembangan, Kementerian Riset, Teknologi, dan Pendidikan Tinggi, Republik Indonesia and accredited in level 3 (SINTA 3), with Decree No.: 29 / E / KPT / 2019. BAREKENG: Jurnal ilmu Matematika dan Terapan was published by: Mathematics Department Faculty of Mathematics and Natural Sciences University of Pattimura Website: http://matematika.fmipa.unpatti.ac.id
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<![CDATA[NONPARAMETRIC REGRESSION MODELING USING THE SPLINE APPROACH TO STUNTING CASES IN INDONESIA ]]>
<![CDATA[Fatekurohman, Mohamat]]>;
<![CDATA[Nur Khasanah, Siti]]>;
<![CDATA[Setia Dewi, Yuliani]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 2 (2025): BAREKENG: Journal of Mathematics and Its Application ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol19iss2pp697-708
<![CDATA[Indonesia is the fourth ranked country in the world and second in Southeast Asia with the highest stunting cases of 21.6%. According to the provisions of the World Health Organization (WHO), the maximum tolerance standard for stunted toddlers is 20 percent or one-fifth of the total number of toddlers, so the stunting rate in Indonesia is still relatively high. The high stunting rate in Indonesia can affect the quality of Indonesia's human resources, so early detection and immediate management of stunted toddlers are needed. Stunting is a condition of failure to grow due to chronic malnutrition which is caused by inadequate nutritional intake for a long time, resulting in being shorter than standard. This research aims to determine several factors that influence stunting in toddlers in Indonesia using the nonparametric spline regression method with one knot, two knots, three knots and the best model is found to be the one knot model. The results of regression nonparametric spline modeling with one knot are GCV of 14.32605 and of 81.1%. From the five variables, namely toddlers receiving complete basic immunization babies receiving exclusive breast milk for 6 months , babies born receiving IMD children aged 6-23 months consuming five of the eight food groups and drink throughout the day , households having access to proper sanitation , the following results were obtained: the variable that don’t have a significant effect was toddlers receiving complete basic immunization , while the other four has a significant effect.]]>
<![CDATA[PRICING EMPLOYEE STOCK OPTION USING TRINOMIAL TREE METHOD ]]>
<![CDATA[Lesmana, Donny Citra]]>;
<![CDATA[Ramadhan, Reza Tri Ahmad]]>;
<![CDATA[Nurjanah, Siti]]>;
<![CDATA[Dharmawan, Vanaya Syahira]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 2 (2025): BAREKENG: Journal of Mathematics and Its Application ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol19iss2pp709-720
<![CDATA[This study explores the Employee Stock Option (ESO) model proposed by Liao and Lyuu, which provides a robust framework for addressing critical factors such as dilution, early exercise, and employee forfeiture rates. The model is solved using the trinomial tree method, allowing for the consideration of three possible stock price movements: increase, unchanged, or decrease. This approach combines forward and backward calculations to accurately evaluate ESO values by accounting for the complex interactions of these parameters. Dilution effects are modeled by adjusting stock prices based on outstanding shares and strike prices, while early exercise probabilities are addressed using a modified Chi-Square distribution to represent employee behavior. Additionally, the forfeiture rate is dynamically adjusted based on ESO returns and the ratio of stock-to-strike prices. The analysis reveals that ESO price negatively correlates with strike price and forfeiture rate, whereas parameters such as vesting time, maturity date, risk-free rate, volatility, and the number of ESOs granted exhibit positive correlations. This comprehensive methodology demonstrates the practical applicability of the Liao and Lyuu model for real-world ESO valuation. By integrating these critical factors into a unified framework, the study contributes significantly to the literature on financial modeling and provides actionable insights for companies seeking to optimize their ESO programs.]]>
<![CDATA[ZERO INFLATED POISSON REGRESSION MODELS TO ANALYZE FACTORS THAT INFLUENCE THE NUMBER OF MEASLES CASE IN JAVA ]]>
<![CDATA[Weni Utomo, Candra R. W. S]]>;
<![CDATA[Efendi, Achmad]]>;
<![CDATA[Wardhani, Ni Wayan Surya]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 2 (2025): BAREKENG: Journal of Mathematics and Its Application ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol19iss2pp721-732
<![CDATA[Measles is an infectious disease that often occurs in children and is caused by the measles virus (morbillivirus) which can cause death. Thus, it is important to identify the factors that cause measles. The number of measles cases is used as response variable in the form discrete data so that Poisson Regression is commonly used. However, some assumptions are sometimes not met, such as overdispersion and excess zero so that can use Zero Inflated Poisson Regression to meet these assumptions. Because the model can overcome two common characteristics that are often found in count data, which are excess zero and overdispersion. The purpose of this study was to determine the factors that influence the number of measles cases in East Java. The data in the study used secondary data obtained from the Central Statistics Agency (BPS). The predictor variables used were the number of population, percentage of vaccination, percentage of poor people, and percentage of adequate sanitation. The results showed that the data is overdispersed because the variance is greater than the mean. There were four predictor variables, The -value of the total population variable is <0.01, the percentage of vaccinations is 0.914, the percentage of poor people <0.01 and the percentage of proper sanitation is 0.014 so it can be concluded that the percentage of vaccinations has no effect on the number of measles cases and the other three variables affect the number of measles cases in East Java. The best model of affect the number of measles cases in East Java is Zero Inflated Poisson with AIC value 326.24. The ZIP model for measles case in East Java is .]]>
<![CDATA[IMPLEMENTATION OF GEOGRAPHICALLY WEIGHTED PANEL REGRESSION WITH GAUSSIAN KERNEL WEIGHTING FUNCTION IN THE OPEN UNEMPLOYMENT RATE MODEL ]]>
<![CDATA[Saska, Indria]]>;
<![CDATA[Sifriyani, Sifriyani]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 2 (2025): BAREKENG: Journal of Mathematics and Its Application ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol19iss2pp733-742
<![CDATA[This study analyzes the factors influencing the Open Unemployment Rate in Kalimantan using the Geographically Weighted Panel Regression (GWPR) model with Gaussian kernel weighting functions. The GWPR model, a local panel regression approach for spatial data, is compared with the global Fixed Effect Model (FEM). Spatial weighting for parameter estimation employs Fixed Gaussian and Adaptive Gaussian kernels, with the optimum bandwidth determined through Cross Validation (CV), resulting in a minimum CV value of 25.536 for the Adaptive Gaussian Kernel. Local factors identified as influencing the Open Unemployment Rate include the Labor Force Participation Rate ( ), Expected Years of Schooling ( ), Average Years of Schooling ( ), Total Population ( ), Number of Poor People ( ), and the Growth Rate of Gross Regional Domestic Product at Constant Prices ( ). The results underscore the importance of spatial heterogeneity in understanding regional unemployment dynamics, as local variations in these factors significantly affect unemployment rates. Moreover, the GWPR model exhibits a notable improvement in predictive accuracy and goodness of fit compared to the global panel regression model, achieving a coefficient of determination of 77.96% and a Root Mean Square Error (RMSE) of 0.2726. These findings highlight the GWPR model's potential in regional economic studies and policymaking, offering precise insights into local determinants of unemployment and facilitating the development of targeted and effective interventions.]]>
<![CDATA[SMALL AREA ESTIMATION OF CHILD UNDERNOURISHMENT PREVALENCE IN BALI AND NUSA TENGGARA ]]>
<![CDATA[Nuriyo, Amalia Ndaru]]>;
<![CDATA[Fajar, Huda Muhammad]]>;
<![CDATA[Novaldi, Jeremia]]>;
<![CDATA[Rahmi, Meautia]]>;
<![CDATA[Miswa, Sabrina Do]]>;
<![CDATA[Sumarni, Cucu]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 2 (2025): BAREKENG: Journal of Mathematics and Its Application ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol19iss2pp743-754
<![CDATA[Children under the age of 17 are particularly prone to undernutrition. Undernutrition can impair children’s growth and development. In the process of policy formulation, it is necessary to calculate a reliable estimate of the prevalence of child undernourishment at the smallest level possible. Using the data of SUSENAS 2023 from BPS, direct estimates at the regency/city level in Bali, West Nusa Tenggara (NTB), and East Nusa Tenggara (NTT) have relative standard error values of over 25% (RSE > 25%), making them less reliable for usage. To solve this, an indirect estimating method known as small area estimation (SAE) can be applied. This study employs SAE HB Lognormal to estimate the prevalence of undernutrition in children. The results of this study show that small area estimation using the HB Lognormal approach improved the reliability of estimates (RSE) of the prevalence of undernutrition in children at the regency/city level in Bali, NTB, and NTT.]]>
<![CDATA[TIME SERIES MODEL FOR TRAIN PASSENGER FORECASTING ]]>
<![CDATA[Hakim, Bashir Ammar]]>;
<![CDATA[Billy, Billy]]>;
<![CDATA[Notodiputro, Khairil Anwar]]>;
<![CDATA[Angraini, Yenni]]>;
<![CDATA[Mualifah, Laily Nissa Atul]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 2 (2025): BAREKENG: Journal of Mathematics and Its Application ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol19iss2pp755-766
<![CDATA[Trains as a means of public transportation have an important role in connecting various regions of Jabodetabek. Therefore, it is necessary to have a deep understanding of the trend of train passenger movements and predict the number of train passengers in the next period in order to optimize the management and service of train passengers properly. In this study, we examine two methods that can be used as forecasting methods for train passenger data sourced from the Central Statistics Agency (BPS), namely ARIMA and Prophet. This study demonstrates that the optimal ARIMA model is ARIMA (0,2,1), achieving a Mean Absolute Percentage Error (MAPE) of 4.91% and a Root Mean Square Error (RMSE) of 1754.970. In addition, the Prophet model, which is an additive regression model designed by Facebook for time series forecasting was also obtained with a MAPE of 0.04% and an RMSE of 1170.59. Considering the MAPE and RMSE values of the two models, the Prophet model emerges as the most suitable for forecasting the number of train passengers in the Jabodetabek region.]]>
<![CDATA[INTRODUCTION TO DOMINO KLEIN-4 GROUP CRYPTOGRAPHY ]]>
<![CDATA[Saragih, Asido]]>;
<![CDATA[Tarigan, Regina Ayunita]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 2 (2025): BAREKENG: Journal of Mathematics and Its Application ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol19iss2pp767-776
<![CDATA[As a type of simple group in mathematics, the concept of the Klein-4 group finds applications in various fields such as biology, 2D materials, games, and more. This research combines the idea of the Klein-4 group with the rules of domino cards to create a binary operation. This binary operation serves as the encryption key, and its inverse serves as the decryption key. The comprehensive process in this study represents a novel application of the Klein-4 group in cryptography. By leveraging the structural properties of the Klein-4 group, this method introduces a unique approach to securing information. The combination of group theory and modular forms in this study enhances the complexity of the encryption and decryption processes, making it more difficult for unauthorized parties to access or interpret the data. As a result, the security of the data is significantly improved. The encryption algorithm is not only efficient but also resistant to common cryptographic attacks. This study demonstrates the potential of abstract algebraic concepts in developing practical solutions for modern-day cryptographic challenges. The research methods and proposed hypotheses in this study have been validated through the proof of the given theorems. However, this study limits the data to alphabet. Researchers interested in the field of cryptography can further develop this idea to apply cryptographic processes to other types of data.]]>
<![CDATA[FORECASTING MONTHLY RAINFALL IN PANGKEP REGENCY USING STATISTICAL DOWNSCALING MODEL WITH ROBUST PRINCIPAL COMPONENT REGRESSION TECHNIQUE ]]>
<![CDATA[Sahriman, Sitti]]>;
<![CDATA[Anisa, Anisa]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 2 (2025): BAREKENG: Journal of Mathematics and Its Application ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol19iss2pp777-790
<![CDATA[A General Circulation Model (GCM) is a global climate model commonly used to predict local-scale climate patterns. However, the spatial resolution of GCMs is typically on a global scale, which is inadequate for predicting local climate. Statistical downscaling (SD) is used to transform climate information from a global scale to a smaller scale for local-scale climate predictions. GCM data have large dimensions and high correlations between grids, so principal component regression (PCR) is used in SD. The minimum covariance determinant (MCD) and minimum vector variance (MVV) methods are used in principal component analysis to obtain robust principal components (PCs). The data used in this study were the monthly rainfall data in Pangkep Regency for the period from January 1999 to December 2022 as the response variable, which were obtained from the Meteorology, Climatology, and Geophysics Agency (BMKG) Region IV Makassar. The predictor variable data were GCM precipitation data (64 variables) for the same period and three dummy variables. This study aimed to obtain rainfall forecasts in Pangkep Regency for the year 2023 based on a robust PCR model using results from MCD and MVV. The modeling results indicated that both the MCD and MVV methods provided similar model accuracy, with a coefficient of determination of approximately 91%. The PCR model with two PCs from the MVV method and dummy variables was identified as the best model for explaining the variability in rainfall data in Pangkep Regency. Additionally, the 2023 rainfall forecast results showed that both methods yielded relatively similar accuracy. The addition of dummy variables in the PCR model improved both the model accuracy and rainfall forecasts. The PCR model with three PCs from MVV and dummy principal component variables produced accurate rainfall forecasts based on a high correlation value (0.974) and the smallest mean absolute percentage error (7.290).]]>
<![CDATA[THE PARTITION DIMENSION OF CYCLE BOOKS GRAPH B_(m,n) WITH A COMMON PATH P_2 ]]>
<![CDATA[Santoso, Jaya]]>;
<![CDATA[Darmaji, Darmaji]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 2 (2025): BAREKENG: Journal of Mathematics and Its Application ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol19iss2pp791-804
<![CDATA[Suppose is a connected graph with elements of a set of vertices denoted by and a subset of . The distance between and is the shortest distance to every vertex in . Let be a partition of , where each subset belongs to . The representation of a vertex with respect to is defined as the set of distances from to each vertex in . If each representation of each vertex of is different, then the partition is called the resolving partition of , and the partition dimension is the smallest integer such that has a resolving partition with members. In this research, we show the partition dimensions of the cycle books graph . Cycle books graph is a graph consisting of copies of a cycle with a common path . The partition dimension of the cycle books graph for and is shown.]]>
<![CDATA[MODELING THE INFLUENCE OF CRUDE OIL PRODUCTION AGAINST INDONESIAN SOLAR WHOLESALE PRICE INDEX WITH LEAST SQUARE SPLINE ESTIMATOR APPROACH ]]>
<![CDATA[Pratiwi, Rosidun Nindyo]]>;
<![CDATA[Fauziah, Nathania]]>;
<![CDATA[Syahputra, Bimo Okta]]>;
<![CDATA[Firmanda, Ahmad Wahyu]]>;
<![CDATA[Amelia, Dita]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 2 (2025): BAREKENG: Journal of Mathematics and Its Application ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol19iss2pp805-818
<![CDATA[Solar plays a crucial role in supporting energy sector activities in Indonesia. The fluctuating price of solar is influenced by crude oil production, as crude oil is the main raw material in solar production. The Russia-Ukraine war, which reached its peak in March 2020, also impacted global oil production, given that Russia is one of the largest oil producers and exporters in the world. This study aims to model the effect of crude oil production on the Solar Wholesale Price Index (SWPI) in Indonesia after the Russia-Ukraine war using the Least Squares Spline estimator approach. This approach was chosen because the relationship between the variables is complex and nonlinear, making linear models unsuitable. The results show that the best model is a nonparametric model with three knot points at a polynomial degree of one, which explains 90.26% of the variability in crude oil production relative to the SWPI. The optimal knot points were selected using the Generalized Cross Validation (GCV) method, resulting in a minimum GCV value of 320.9889. Crude oil production was found to have a significant effect on the SWPI and meets the classical assumption tests. However, this study has limitations, as it only considers the effect of crude oil production without including other external factors, such as energy policies or geopolitical influences. Additionally, the model still has limitations in capturing more complex relationship patterns. This study offers an original contribution through the application of the Least Squares Spline estimator approach, which has not been widely used before in analyzing the relationship between crude oil production and SWPI in Indonesia. For future research, it is recommended that the model be expanded by considering more knot points and higher polynomial degrees to capture more complex relationship patterns between these variables.]]>
