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[CRAMER’S RULE IN MIN-PLUS ALGEBRA ]]>
<![CDATA[Zakia Nur Ramadhani Putri]]>;
<![CDATA[Siswanto Siswanto]]>;
<![CDATA[Vika Yugi Kurniawan]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol18iss2pp1147-1154
<![CDATA[Cramer’s rule is one of a method for solving a system of linear equations in conventional algebra. The system of linear equation can be solved using Cramer’s rule if . Max-plus algebra is a set where is a set of real numbers, equipped with biner operations and where and . Min-plus Algebra is a set where is a set of real numbers, equipped with biner operations and where and . In max-plus algebra has been formulated Cramer’s rule to solve a system of linear equations. Because max-plus algebra is isomorphic to min-plus algebra, Cramer’s rule can be formulated into min-plus algebra. The purpose of this research is to determine the sufficient conditions for a system of linear equations can be solved using Cramer’s rule. The method used in this research is a literature study that reviews previous research related to min-plus algebra, max-plus algebra, and Cramer’s rule in max-plus algebra. By using the appropriate analogy in max-plus algebra, we can determine the sufficient conditions so that a system of linear equations in min-plus algebra can be solved using Cramer’s rule. Based on the research, the sufficient conditions for a system of linear equations can be solved using Cramer’s rule are for and with the Cramer’s rule is . For an invertible matrix A, Cramer’s rule can be written as .]]>
<![CDATA[COMBINATION OF ETHNOMATHEMATICS AND THE MOZART EFFECT TO IMPROVE PROBLEM-SOLVING SKILLS AND MATHEMATICAL DISPOSITION ]]>
<![CDATA[Dianne Amor Kusuma]]>;
<![CDATA[Budi Nurani Ruchjana]]>;
<![CDATA[Sri Adi Widodo]]>;
<![CDATA[Estiyan Dwipriyoko]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol18iss2pp1155-1166
<![CDATA[The background of this research is that student learning outcomes in analytical geometry lecture during the transition from pandemic to Covid-19 endemic are still low, which is due to a lack of student interest in learning, and they are still accustomed to online learning, thus having an impact on their low problem-solving skills and mathematical disposition. This research aims to determine to what extent the implementation of ethnomathematics and the Mozart effect can improve students' problem-solving skills and mathematical disposition in analytical geometry lecture during the transition from pandemic to endemic COVID-19, so the research is important to do. The implementation of ethnomathematics and the Mozart effect in mathematics learning is unique because it is a combination of learning approaches that have never been used before in Indonesia and other countries. The research method used was a quasi-experimental non-equivalent control group design because this research was experimental and sample determination was not carried out randomly, but using purposive sampling technique on the second-semester students of the mathematics undergraduate program, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran. The instruments used in this study were problem-solving skills test, mathematical disposition scale, and students’ attitude questionnaire toward learning with the implementation of ethnomathematics and the Mozart effect. The results showed that: (1) problem-solving skills of students who received learning by implementing ethnomathematics and the Mozart effect are better than students who achieved direct instruction; (2) mathematical disposition of students who received learning by implementing ethnomathematics and the Mozart effect is better than students who achieved direct instruction; and (3) students are interested and motivated to learn mathematics by implementing ethnomathematics and the Mozart effect. This research concludes that the implementation of ethnomathematics and the Mozart effect can improve students' problem-solving skills and mathematical disposition in analytical geometry lecture during the transition period from the pandemic to endemic COVID-19. It can be seen from good average post test scores achieved by students.]]>
<![CDATA[PROVINCIAL CLUSTERING BASED ON EDUCATION INDICATORS: K-MEDOIDS APPLICATION AND K-MEDOIDS OUTLIER HANDLING ]]>
<![CDATA[Octavia Rahmawati]]>;
<![CDATA[Achmad Fauzan]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol18iss2pp1167-1178
<![CDATA[K-Medoids is a clustering algorithm that is often used because of its robustness against outliers. In this research, the focus is to cluster provinces based on educational level through several assessment indicators. This is in line with improving the quality of education in point 4 of the National Sustainable Development Goals (SDGs), namely "Quality Education". One of the points of the National Sustainable Development Goals (SDGs) that will still be improved is "Quality Education" which is the 4th point. This is because the success of a country is determined by the quality of good education. The condition of education in Indonesia still overlaps, so it is necessary to do equal distribution of education through clustering. The purpose of this research is to provide the best cluster results according to the Silhouette Index, which then the results of the clustering can be used as a consideration for advancing education in areas that still need attention, through policies or programs that can be developed by educational observers. This research was conducted in 34 provinces in Indonesia. The data source is from Statistical Publications by BPS RI. The method used is K-Medoids, because in this study there were outliers found. In addition to natural K-Medoids, the researcher also wants to compare methods by implementing K-Medoids with outlier handling in the form of imputed mean values and K-Medoids with imputed min-max values. The Silhouette Index results and cluster formation for the three comparators were 0.24 with 2 clusters, 0.26 with 8 clusters and 0.25 with 9 clusters, respectively. What differentiates this research from previous research is the type of outlier handling. Generally, K-Medoids are very indifferent to the existence of outliers. K-medoids is a widely recognized and straightforward clustering approach. Nevertheless, the algorithm's effectiveness might occasionally decline as a result of local outliers and the random selection of beginning medoids]]>
<![CDATA[ANALYSIS AND OPTIMAL CONTROL OF HIV GROWTH MODEL IN THE BODY WITH ANTIRETROVIRAL THERAPY ]]>
<![CDATA[Erlyana Trie Damayanti]]>;
<![CDATA[Chairul Imron]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol18iss2pp1179-1188
<![CDATA[Human Immunodeficiency Virus (HIV) is a virus that affects the human immune system. HIV infection causes a decrease in the body's immunity because the virus attacks immune-building cells, especially T-CD4 cells. Currently, there is no treatment that can cure or eliminate HIV, but antiretroviral therapy can be done. This study discusses the growth model of HIV in the body that is given control in an effort to maximize healthy T-CD4 cells. In this model, the infection-free and infected equilibrium points are also discussed and their stability is analyzed. Then the optimal control is solved using the Pontryagin Maximum Principle method and solved numerically using the fourth-order Runge Kutta method. Based on the analysis and simulation results, the system is asymptotically stable around the infection-free equilibrium point and unstable around the infected equilibrium point. Simulation results show that with the control of antiretroviral therapy, the T-CD4 cell population grows significantly which can improve the quality of life of patients. And the growth of HIV in the body can be inhibited until it cannot reproduce itself.]]>
<![CDATA[ANALYSIS AND OPTIMAL CONTROL OF TUBERCULOSIS DISEASE SPREAD MODEL WITH VACCINATION AND CASE FINDING CONTROL (CASE STUDY: SURABAYA CITY) ]]>
<![CDATA[Dinda Anisa' Maulina]]>;
<![CDATA[Chairul Imron]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol18iss2pp1189-1200
<![CDATA[Tuberculosis is a contagious disease that infects humans. It is caused by the bacterium Mycobacterium tuberculosis (M.tb). It is the largest infectious disease in the world and has become a major global health problem. Therefore, efforts are being made to control the spread of tuberculosis disease through vaccination and case finding, with the aim of reducing the population of latently infected and actively infected individuals. This study discusses the mathematical model of tuberculosis disease spread, disease-free and endemic equilibrium points, and stability analysis around the equilibrium points. Then, using Pontryagin's minimum principle, the optimal control problem is solved numerically by the 4th-order Runge-Kutta method. Based on the analysis and simulation results, the system is asymptotically stable around the disease-free and endemic equilibrium points. Furthermore, optimal control in the form of vaccination of susceptible individuals is required to further suppress the rate of change of susceptible individuals into latent individuals, while control in the form of case finding on latently infected individuals is required until the 9th year to minimize the population size, while on actively infected individuals, it is required until the 8th year to minimize the population size. Providing optimal control resulted in a 100% increase in the susceptible population and a 100% reduction in the latent and infected populations.]]>
<![CDATA[MODELLING CRIME RATES IN INDONESIA USING TRUNCATED SPLINE ESTIMATOR ]]>
<![CDATA[Muhammad Althof Juniar]]>;
<![CDATA[Azzahra Fania]]>;
<![CDATA[Diana Ulya]]>;
<![CDATA[Rico Ramadhan]]>;
<![CDATA[Nur Chamidah]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol18iss2pp1201-1216
<![CDATA[Criminal acts are actions that violate the law and can arise from various factors such as emotions, psychological pressure, and others. Crime rate is a number that indicate the level of crime vulnerability in a certain area at a certain time. Higher crime rates correspond to increased vulnerability in an area, and vice versa. Among various forms of criminal acts, the number of criminal acts and narcotics crimes in Indonesia tends to increase in 2020 and 2021. The aim of the research is to identify the characteristics of crime rate data based on the number of decency and narcotics incidents in Indonesia using a nonparametric regression approach. This research uses a nonparametric regression method spline truncated and linear regression as comparison. It was found that West Papua Province has the highest crime rate, based on a comparison between linear regression model and truncated spline nonparametric regression model, it can be concluded that the best model is the truncated spline nonparametric regression model with a Generalized Cross Validation (GCV) of 2468.487 and a coefficient of determination of 0 .7389091, indicating that approximately 73% of the variability of the dependent variable can be explained by the independent variables included in the model.]]>
<![CDATA[ANALYSIS OF RELATIONSHIP BETWEEN THE USAGE OF ONLINE LOAN SERVICES AND THE WELL-BEING OF INDONESIAN USING CHI-SQUARE TEST ]]>
<![CDATA[Nur Chamidah]]>;
<![CDATA[Nadhira Safa Kamiilah]]>;
<![CDATA[Putu Eka Andriani]]>;
<![CDATA[Cynthia Anggelyn Siburian]]>;
<![CDATA[Muhammad Rizaldy Baihaqi]]>;
<![CDATA[Salma Bethari Andjani S]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol18iss2pp1217-1228
<![CDATA[Online fintech lending offers convenience by providing flexibility for both lenders and borrowers. It led to a significant increase in users. Despite this encouraging growth, it comes with risks, such as the emergence of illegal loan companies. The controversial positive and negative aspects of online loans have sparked the researchers' interest in understanding how the Indonesian public perceives the existence of online loans and whether there is a relationship between the use of online loans and the well-being of users. The data were collected through the questionnaire using Google Form and then distributed to respondents who meet the specified sample criteria, namely Indonesian, aged 17 years old or above, and still able to think rationally. The total study sample are 191 respondents, with the total male is 90 and the total female is 101. Since the results of the data gathered were in the form of categorical data, so the Chi-square test is utilized in this study. With the calculated chi-square less than the chi-square table, it showed that there is no correlation between the frequency of using online loan services and the well-being of the Indonesian people, whether based on age, level of education, or type of job. Hence, it can be concluded that the usage of online loan services is not influences the well-being of Indonesian. It is also known that public perceptions of online loans vary and cannot be generalized. However, those less prosperous, tend to agree with and appreciate the online loan services’ existence compared to those who are prosperous.]]>
<![CDATA[THE UNINFORMATIVE PRIOR OF JEFFREYS’ DISTRIBUTION IN BAYESIAN GEOGRAPHICALLY WEIGHTED REGRESSION ]]>
<![CDATA[Fachri Faisal]]>;
<![CDATA[Henny Pramoedyo]]>;
<![CDATA[Suci Astutik]]>;
<![CDATA[Achmad Efendi]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol18iss2pp1229-1236
<![CDATA[When using the Bayesian method for estimating parameters in a geographically weighted regression model, the choice of the prior distribution directly impacts the posterior distribution. The distribution known as the Jeffreys prior is an uninformative type of prior distribution and is invariant to reparameterization. In cases where information about the parameter is not available, the Jeffreys' prior is utilized. The data was fitted with an uninformative Jeffreys' prior distribution, which yielded a posterior distribution that was utilized for estimating parameters. This study aims to derive the prior and marginal posterior distributions of the Jeffreys' and in Bayesian geographically weighted regression (BGWR). The marginal posterior distributions of and can be obtained by integrating the other parameters of a common posterior distribution. Based on the results and discussion, the Jeffreys prior in BGWR with the likelihood function is . On the other hand, the marginal posterior distribution of follows a normal multivariate distribution, that is, , while the marginal posterior distribution of follows an inverse gamma distribution, that is, . As further research, it is necessary to follow up on several limitations of the results of this research, namely numerical simulations and application to a particular case that related to the results of the analytical studies that we have carried out.]]>
<![CDATA[ENSEMBLE CNN WITH ADASYN FOR MULTICLASS CLASSIFICATION ON CABBAGE PESTS ]]>
<![CDATA[Nabila Ayunda Sovia]]>;
<![CDATA[Ni Wayan Surya Wardhani]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol18iss2pp1237-1248
<![CDATA[Image classification is a complex process influenced by various factors, one of which is the amount of image data. In the context of cabbage pest classification, data often exhibits a significant class imbalance, where certain pests are more prevalent than others. This imbalance can pose challenges during model training and evaluation, potentially leading to biases in favor of the majority pests and reduced accuracy in identifying and classifying the less common ones. This research aims to enhance the classification performance for multiclass data specific to cabbage pests. We propose an ensemble learning approach that combines Convolutional Neural Network (CNN), Support Vector Machine (SVM), and Bagging methods. To address the imbalance issue inherent in cabbage pest data, we employ the Adaptive Synthetic Sampling (ADASYN) resampling technique. The CNN acts as the primary image identifier and classifier for various cabbage pests. Subsequently, the CNN model is integrated into SVM and Bagging models to mitigate the challenges of imbalanced data in pest classification. The research outcomes demonstrate that our ensemble approach, in conjunction with the ADASYN resampling technique, achieves an impressive accuracy rate of 97%, signifying its potential for improved cabbage pest detection and classification.]]>
<![CDATA[MODELING CHRONIC FILARIASIS CASES IN WEST JAVA USING A MULTIVARIATE ADAPTIVE APPROACH REGRESSION SPLINES ]]>
<![CDATA[Ardi Kurniawan]]>;
<![CDATA[Mochammad Firmansyah]]>;
<![CDATA[Toha Saifudin]]>
<![CDATA[ BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application ]]>
Publisher : <![CDATA[PATTIMURA UNIVERSITY ]]>
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DOI: 10.30598/barekengvol18iss2pp1249-1260
<![CDATA[One of the most crippling infectious diseases in the world is filariasis. Indonesia is a unitary country with 34 provinces, where West Java is one of the 5 provinces with the most filariasis sufferers in Indonesia as of 2021. Reinfection occurs in places that have implemented POMP. Therefore, monitoring operations must be carried out to track the emergence of new cases and risk factors for transmission. The aim of this research focuses on describing and modeling the number of chronic filariasis in West Java, as well as interpreting the best model results obtained. The method used is a method with a nonparametric regression approach, namely Multivariate Adaptive Regression Spline. The results of the research show that the best model obtained is a combination of 15 base functions, maximum interaction 2, and minimum observation between knots 1. From this model, the predictor variable that has the most influence on the response variable in order based on the level of variable importance is the Percentage of Population Access to Facilities Decent Sanitation, Percentage of Households with Clean and Healthy Behavior (PHBS), Sex Ratio, and Percentage of Poor Population. The interpretation of the best model is that the variable Percentage of Population Access to Adequate Sanitation Facilities above 6,650% will contribute to a reduction in the number of chronic filariasis; the Sex Ratio variable below 103,300 will contribute in the form of a reduction in the number of chronic filariasis. it can be seen that the predictor variable that has the most influence on the response variable is the variable Percentage of Population Access to Proper Sanitation Facilities with an importance level of 100%.]]>
