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JTAM (Jurnal Teori dan Aplikasi Matematika)
Published by Universitas Muhammadiyah Mataram
ISSN : 25977512     EISSN : 26141175     DOI : 10.31764/jtam
Core Subject : Education,
Mathematics
Jurnal Teori dan Aplikasi Matematika (JTAM) dikelola oleh Program Studi Pendidikan Matematika FKIP Universitas Muhammadiyah Mataram dengan ISSN (Cetak) 2597-7512 dan ISSN (Online) 2614-1175. Tim Redaksi menerima hasil penelitian, pemikiran, dan kajian tentang (1) Pengembangan metode atau model pembelajaran matematika di sekolah dasar sampai perguruan tinggi berbasis pendekatan konstruktivis (PMRI/RME, PBL, CTL, dan sebagainya), (2) Pengembangan media pembelajaran matematika berbasis ICT dan Non-ICT, dan (3) Penelitian atau pengembangan/design research di bidang pendidikan matematika, statistika, analisis matematika, komputasi matematika, dan matematika terapan.
Arjuna Subject : -
Articles 540 Documents
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Matric Flux Potential in Time Independent Infiltration Problems from a Single Triangular and a Trapezoidal Irrigation Channel Munadi, Munadi; Rokhman, Moh. Shaefur; Oktaviani, Dian Nataria; Ahmadi, Ahmadi; Jannah, Helmi Roichatul
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 1 (2024): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i1.17033

Abstract

In this paper, steady infiltration problems into a homogeneous soil from a single triangular and trapezoidal irrigation channel are considered. The governing equation is Richard's equation that represents the movement of water in unsaturated soil. It is a non-linear equation and can be solved by linearizing to become a modified Helmholtz equation. Dual Reciprocity Boundary Element Methods (DRBEM) are used in this study to numerically solve the modified Helmholtz equation. Therefore, by using a provided solution, the numerical Matric Flux Potential (MFP) is calculated. This method was applied to the homogeneous soil problem of stationer infiltration from triangular and trapezoidal single irrigation. Both numerical solutions were compared. The result show that the MFP value from the triangular irrigation is higher than the trapezoidal irrigation. This indicates that content water from the triangular irrigation channel is higher than the trapezoidal irrigation channel. 
Selection Dominant Features Using Principal Component Analysis for Predictive Maintenance of Heave Engines Trihandaru, Suryasatriya; Parhusip, Hanna Arini; Heriadi, Adrianus Herry; Santosa, Petrus Priyo; Sardjono, Yohanes; Lea, Lea
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 4 (2024): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i4.22854

Abstract

This article aims to identify the dominant features that have a significant impact on the health of a heavy machine that relates to the digital infrastructure of a company. The importance of this research is that the authors define predictive maintenance based on Principal Component Analysis (PCA), which is the novelty of this article. The novel contribution of this research lies in the application of Principal Component Analysis (PCA) for predictive maintenance of heavy machinery, which has not been integrated into the Scheduled Oil Sampling (SOS) procedures. The recorded data are called Scheduled Oil Sampling (SOS) and historical data from an equipment called CoreDataQ, which works for recording many features from heavy machine activities. The data contain two sets data. The method is Principal Component Analysis (PCA). This method leads to obtain a maximum of 20 significant features on data based on SOS. The results have been confirmed and agreed upon by the manager who owned CoreDataQ to consider the selected dominant features for further related maintenance. 
Development of Differentiate Student Worksheets: an Efforts to Improve Student Argumentation Ability Putra, Zuhadur Ra'is Ariyono; Rahardi, Rustanto; Sisworo, Sisworo
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 1 (2024): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i1.17426

Abstract

Online learning experiences have been associated with reduced learning outcomes and limited student engagement in argumentation. To address this issue, the focus on teaching materials becomes crucial, especially in promoting differentiated learning to accommodate pandemic-induced learning losses. A prime candidate for enhancing argumentation skills is the study of quadrilaterals within mathematics. Mastering the quadrilateral concept and its argumentative structure is pivotal for students. Hence, the creation of student worksheets employing differentiated learning principles is imperative. This research aims to develop valid, practical, and effective quadrilateral worksheets with a focus on adversity quotient differentiation. The ADDIE model guides the development process through Analysis, Design, Development, Implementation, and Evaluation stages. Rigorous evaluation, including expert validation (83.8% very valid), field trials (91% very practical), and N-Gain score analysis (0.73, indicating effectiveness), underscores the quality of the developed worksheets. In conclusion, the adversity quotient differentiated quadrilateral worksheets has been successfully crafted to enhance students' argumentation skills. It is deemed valid, practical, and effective in improving learning outcomes. This initiative holds potential for addressing the challenges posed by online learning and contributes to students' academic development.
Chi-Square Feature Selection with Pseudo-Labelling in Natural Language Processing Afriyani, Sintia; Surono, Sugiyarto; Solihin, Iwan Mahmud
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 3 (2024): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i3.22751

Abstract

This study aims to evaluate the effectiveness of the Chi-Square feature selection method in improving the classification accuracy of linear Support Vector Machine, K-Nearest Neighbors and Random Forest in natural language processing when combined with classification algorithms as well as introducing Pseudo-Labelling techniques to improve semi-supervised classification performance. This research is important in the context of NLP as accurate feature selection can significantly improve model performance by reducing data noise and focusing on the most relevant information, while Pseudo-Labelling techniques help maximise unlabelled data, which is particularly useful when labelled data is sparse. The research methodology involves collecting relevant datasets, thus applying the Chi-Square method to filter out significant features, and applying Pseudo-Labelling techniques to train semi-supervised models. In this study, the dataset used in this research is the text data of public comments related to the 2024 Presidential General Election, which is obtained from the Twitter scrapping process. The characteristics of this dataset include various comments and opinions from the public related to presidential candidates, including political views, support, and criticism of these candidates. The experimental results show a significant improvement in classification accuracy to 0.9200, with precision of 0.8893, recall of 0.9200, and F1-score of 0.8828. The integration of Pseudo-Labelling techniques prominently improves the performance of semi-supervised classification, suggesting that the combination of Chi-Square and Pseudo-Labelling methods can improve classification systems in various natural language processing applications. This opens up opportunities to develop more efficient methodologies in improving classification accuracy and effectiveness in natural language processing tasks, especially in the domains of linear Support Vector Machine, K-Nearest Neighbors and Random Forest well as semi-supervised learning.
The Development of Students’ Worksheets Based on Combinatoric Reasons in Elementary School Aini, Nurul; Suryowati, Eny
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 2 (2024): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i2.20214

Abstract

This study was motivated by the many shortcomings of students’ worksheets so far, including the incapability in developing students’ scientific skills and high-level thinking. Meanwhile, the learning objectives of the elementary school level get students to think reasonably and solve problems. Therefore, developing students’ worksheets based on combinatoric reason is the solution, as it drills students to have sustainable thinking. This study aimed to see the validity, practicality, and effectiveness of students’ worksheets based on combinatoric reason. It is a Research and Development study with the Plomp model. The plomp model consists of preliminary investigation; design;  realization/construction; and test, evaluation, and revision. The research instruments were students’ worksheets, validation form, questionnaire, and test form. The subject involved 40 students in the sixth grade of elementary school. The data analysis used is descriptive qualitative and descriptive quantitative.  It resulted in 91,5% for the validity (very valid), 90,9% for the practicality (very practical), and 92,5% for the effectiveness (very effective). Thus, it indicates that students’ worksheets based on combinatoric reason are valid, practical, and effective, which are proper for elementary school. So, it is recommended that mathematics teachers use it in learning, because it trains students to use combinatorial reasoning. As a result, students become flexible and logical in determining strategies, as well as being systematic in solving problems. As a result, elementary school students' Problem-solving and higher order thinking abilities become better.
Hyperstructures in Chemical Hyperstructures of Redox Reactions with Three and Four Oxidation States Agusfrianto, Fakhry Asad; Andromeda, Sonea; Hariri, Mariam
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 1 (2024): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i1.17011

Abstract

Hyperstructures find numerous applications across various disciplines. One notable application is in chemistry, particularly in the context of chemical reactions. In 2014, Davvaz introduced the concept of bi-hyperstructures, but their application specifically in chemical reactions, has yet to be thoroughly explored in previous studies. Thus, the primary aim of this paper is to examine and analyze the different types of bi-hyperstructures present within chemical hyperstructures. The scope of this study focuses on two types of chemical hyperstructures: redox reactions and reactions in electrochemical cells. Within these chemical hyperstructures, we investigate the possibility of bi-hyperstructures among bi-semihypergroups, bi-hypergroups, bi-H_v-semigroups, and bi-H_v-groups. Next, some properties of bi-hyperstructures related to hyperstructures are also investigate.
Modelling of Forecasting ASEAN-5 Stock Price Index Using GSTAR Model Zakiyah, Tuti; Windasari, Wahyuni
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 3 (2024): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i3.22738

Abstract

This research aims to apply the Generalized Space-Time Autoregressive (GSTAR) model to predict stock price indices in ASEAN-5 countries. Generalized Space Time Autoregressive (GSTAR) model is one of the most common used space-time model to modeling and predicting spatial and time series data. The GSTAR model produces a space-time model that adopts the stages of the Autoregressive Integrated Moving Average (ARIMA) model. This research uses parameter estimation using the Maximum Likelihood method, which is a method used to estimate parameter values by maximizing the probability function seen based on observations. This research uses secondary data in the form of Stock Price Index data from 5 countries in Asia, namely the Composite Stock Price Index (JCI), Philippine Stock Exchange (PSEi), Strait Time Index (STI), Kuala Lumpur Composite Index (KLCI), and Thailand Stock Exchange Index (SETI). Stock Price Index data was divided into in-sample data for Generalized Space-Time Autoregressive (GSTAR) modelling and out-sample data used to validate presumptive results. In-sample data was taken from January 4, 2021, to December 29, 2023, and then out-sample data for presumptive was as many as 5 from January 2, 2024, to January 8, 2024. From the modeling results, it was found that the mean MAPE value of the GSTAR model was smaller than that of the ARIMA model. Moreover, based on the presumptive results for the following 5 periods using the GSTAR (2.1) I(1) model, a Mean Absolute Percentage Error (MAPE) of less than 10% in each location. The values shows that GSTAR model is more accurate than the ARIMA model.
Improvement of Real-GJR Model using Jump Variables on High Frequency Data Nugroho, Didit Budi; Wulandari, Nadya Putri; Alfagustina, Yumita Cristin; Parhusip, Hanna Arini; Tita, Faldy; Susanto, Bambang
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 4 (2024): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i4.24294

Abstract

Volatility is a key indicator in assessing risk when making investment decisions. In the world of financial markets, volatility reflects the degree to which the value of a financial asset fluctuates over a given period. The most common way to measure the future loss potential of an investment is through volatility. Focusing on the Realized GJR (RealGJR) volatility model, which consists of return, conditional volatility, and measurement equations, this study proposes the RealGJR-CJ model developed by decomposing the exogenous variable in the volatility equation of RealGJR into continuous C and discontinuous (jump) J variables. The decomposition of exogenous variables makes the RealGJR-CJ model follow realistic financial markets, where the asset volatility is a continuous process with some jump components. As an empirical illustration, the models are applied to an index in the Japanese stock market, namely Tokyo Stock Price Index, covering from January 2004 to December 2011. The observed exogenous variable in the volatility equation of RealGJR models is Realized Volatility (RV), which is calculated using intraday data with time intervals of 1 and 5 minutes. Adaptive Random Walk Metropolis method was employed in Markov Chain Monte Carlo algorithm to estimate the model parameters by updating the parameters during sampling based on previous samples from the chain. From the results of running the MCMC algorithm 20 times, the mean of the information criteria of competing models is significantly different based on standard deviation and the result suggests that the model with continuous and jump variables can improve the model without jump. The best fit model is provided by RealGJR-CJ with the adoption of 1-minute RV data. 
Projection of PT Aneka Tambang Tbk Share Risk Value Based on Backpropagation Artificial Neural Network Forecasting Result Haris, M. Al; Setyaningsih, Laras Indah; Fauzi, Fatkhurokhman; Amri, Saeful
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 2 (2024): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i2.20267

Abstract

PT Aneka Tambang Tbk (ANTAM) received an award as the most sought-after stock issuer in Indonesia in 2016. That stock continued to attract investors in 2022 due to a 105% increase in net profit and a 19% increase in sales from the previous year. Despite the upward trend, investors still had doubts due to the fluctuating movement of ANTAM's stock prices. Therefore, forecasting was needed to determine the future movement of stock prices. The Backpropagation Neural Network method had good capabilities for fluctuating data types. However, this method has the disadvantage of a lengthy iteration process. To handle this limitation, The Nguyen-Widrow weighted setting was applied to address this constraint. The expected Shortfall (ES) method used the forecasting results to measure investment risk. This research uses ANTAM stock closing price data from May 2, 2018, to May 31, 2023. Based on the analysis results, the best architecture was obtained with a configuration of 5-11-1, using Nguyen-Widrow weight initialization and a combination of a learning rate of 0.5 and momentum of 0.9. This architecture yielded a prediction error based on the Mean Absolute Percentage Error (MAPE) of 1.9947%. Risk measurement with the ES method based on the prediction for the next 60 periods showed that at a 95% confidence level, the risk value was 0.002181; at a 90% confidence level, it was 0.002165; at an 85% confidence level, it was 0.002148, and at an 80% confidence level, it was 0.002132.
Algorithm for Constructing Total Graph of Commutative Ring Meinawati, Rima; Kurniawan, Vika Yugi; Kurdhi, Nughthoh Arfawi
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 2 (2024): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i2.19850

Abstract

Let R be a commutative ring. The total graph of R, denoted by TΓ(R) is a graph whose vertices are all elements of the ring R and every i,j∈R with i≠j, then i and j vertices are connected by edges if and only if i+j∈Z(R), where Z(R) is the set of zero-divisors in R with 0∈Z(R). Python programming is code that is easy to learn, read, understand, and helpful in explaining problems regarding graphs and algebra. In this paper, we determine an algorithm to construct the total graph of ring Z_n using Python. The research methods in this paper is a literature studies. The results generated by the algorithm can be utilized to observe the characteristic patterns displayed by the graph. Based on the algorithm’s constructed graph pattern, several properties of TΓ(Z_n ) can be inferred. For instance, if n is a prime number, then TΓ(Z_n ) is a disconnected graph. On the other hand, if n is a prime number and n≥3, then TΓ(Z_2n ) and TΓ(Z_4n ) is a connected graph, regular graph, Hamiltonian graph, and has a girth gr(TΓ(〖Z〗_n ))=3. In this paper we creating an algorithm to construct total graphs from commutative rings streamlines the construction process, enhances accessibility and utilization of total graphs, and supports parameter variation exploration and application in problem-solving. 

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