JTAM (Jurnal Teori dan Aplikasi Matematika)

Panel Data Spatial Regression Modeling with a Rook Contiguity Weighting Function on the Human Development Index in West Sumatera Province

Prizka Rismawati Arum — 2024-01-19

The achievement of the level of welfare of a region or country can be seen from the level of human development as measured by the Human Development Index (HDI). West Sumatra is one of the provinces with HDI achievements above the national average. However, there are still regencies/cities in West Sumatra Province that have HDI achievements below the national average and HDI achievements in West Sumatra Province Regencies/Cities have changed in 2017-2021. Therefore, in this study, spatial analysis of panel data was used. The aim of this research is to find out the general description of the HDI of West Sumatra Province, obtain a panel data spatial regression model and obtain variables that significantly influence on HDI in West Sumatra Province 2017â”€2021because differences in HDI achievement were suspected to have influences from areas that were side by side and the area was observed more than once. The model formed from this analysis using the rook contigutiy weighting function is Random Effect Spatial Autoregressive because the spatial interactions formed in human development index data in West Sumatra Province are real at lag. This model is a suitable model based on panel spatial model selection and has an R2 value of 92.94%. Analysis of human development index data in regencies/cities in West Sumatra Province using spatial regression panel data obtained results that expectations of school length (X1), average length of schooling (X2), and population density (X3) significantly directly influenced the human development index in regencies/cities in West Sumatra Province.

Ratio Interval-Frequency Density with Modifications to the Weighted Fuzzy Time Series

Etna Vianita — 2024-01-19

The improvement of plantation forecasting accuracy, particularly with regard to coffee production, was an essential aspect of earth observations for the purpose of informing plantation management alternatives. These decisions included strategic and tactical decisions on supply chain operations and financial decisions. Many research initiatives have used a variety of methodologies to the forecasting of plantation areas and related industries, such as coffee production. One of these methods was known as the fuzzy time series (FTS) technique. ThisÂ study combined ratio-interval and frequency density to get universe of discourse and partition followed by adopted weighted and modified that weighted. The first step was defined universe of discourse using ratio-interval algorithm. The second step was partition the universe of discourse using ratio-interval algorithm followed by frequency density partitioning. The third step was fuzzyfication. The fourth step built fuzzy logic relationship (FLR) and fuzzy logic relationship group (FLRG). The fifth step was adopted the modification weighted. The last step was defuzzyfication. TheÂ models evaluatedÂ byÂ averageÂ forecastingÂ errorÂ rateÂ (AFER)Â andÂ comparedÂ withÂ existing methods.Â AFERÂ valueÂ 1.24%Â forÂ proposed method.

Partial Fourier Transform Method for Solution Formula of Stokes Equation with Robin Boundary Condition in Half-space

Sri Maryani — 2024-01-19

The area of applied science known as fluid dynamics studied how gases and liquids moved. The motion of the fluid in the liquid and vapour phases is described by a special system of partial differential equations. The research purpose of this article investigated the solution formula of incompressible Stokes equation with the Robin boundary condition in half-space case. The solution formula for Stokes equation was calculated using the partial Fourier transform. This calculation was carried out over the Weisâ€™s multipliers theorem. Our calculation showed that the solution formula of Stokes equation with Robin boundary condition in half-space for velocity and pressure were contained multipliers as due to work Shibata & Shimada. Due to our consideration of the half-space situation, the partial Fourier transform approach is the most appropriate one to use to get the velocity and pressure for the Stokes equation with Robin boundary condition. Furthermore, research methods in this article, in the first stage, we use the resolvent problem of the model. Secondly, we apply the partial Fourier transform to the model problem and finally, we use inverse partial Fourier transform to get the solution formula of the incompressible type of Stokes equation for velocity and pressure. This result indicates that Weis' multiplier theorem also allows us to find the local well-posedness of the model problem in addition to the maximal Lp-Lq regularity class (Gerard-Varet et al., 2020).

Fuzzy Logic Speed Regulator for D.C. Motor Tuning

Wasim Raza — 2024-01-19

A D.C. motor's rotational speed is regulated in this study using a PID controller and a fuzzy logic controller. In contrast to the fuzzy logic controller, which uses rules based on knowledge and experience, the proportional-integral-derivative (PID) controller requires a mathematical system model.Â Â This study investigates the regulation of a DC motor's velocity using PID and fuzzy logic controllers. The PID controller utilizes a mathematical model and parameter tuning by trial and error. Still, the fuzzy logic controller (FLC) operates on rule-based knowledge, enabling it to handle the nonlinear features of the DC motor effectively. The FLC design entails intricate determinations, including the establishment of a rule base and the process of fuzzification. A total of 49 fuzzy rules have been devised to achieve precise control. Based on MATLAB/SIMULINK simulations, the study concludes that the Fuzzy Logic Controller (FLC) beats the Proportional-Integral-Derivative (PID) controller. The FLC exhibits superior transient and steady-state responses, shorter response times, reduced steady-state errors, and higher precision. This study emphasizes the efficacy of the FLC (Fuzzy Logic Controller) in dealing with the difficulties associated with DC motor control. It presents a strong argument for the suitability and efficiency of FLCs in industrial environments compared to conventional PID (Proportional-Integral-Derivative) controllers. There are a wide variety of ways to construct a fuzzy logic controller. The speed error and the rate of change in the speed error are two inputs to the FLC. Defuzzification is done by focusing on the core of the problem. The results show that FLC is superior to PID controllers in efficiency and effectiveness due to its reduced transient and steady-state factors.

Hyperstructures in Chemical Hyperstructures of Redox Reactions with Three and Four Oxidation States

Fakhry Asad Agusfrianto — 2024-01-19

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.

Development of Problem-Solving-Based Digital Learning Media for Flat-Sided 3D Geometry in Junior High School

Pandu Aditya — 2024-01-19

Mastery of concepts is necessary for students in learning geometry, particularly in the topic of flat-sided 3D spatial structures. A strong grasp of concepts is achieved through non-routine problem-solving exercises, which are an integral part of problem-solving-based learning. According to the OECD (Organisation for Economic Co-operation and Development) of Education and Skills 2030, problem-solving-based learning is considered an important component in the curriculum of 60% of countries worldwide. The use of digital media is an innovative approach in education that can transform abstract geometric forms into real-world situations. The focus of this research is to develop digital media to enhance conceptual understanding among eighth-grade students at Yosowinangun Junior High School. The outcome of this study is a valid, practical, and effective digital learning medium for improving conceptual understanding. The research adopts the ADDIE model as the methodological framework. The research sample consists of twenty eighth-grade students. Data collection instruments include validation sheets, practicality questionnaires, interviews, and tests. The research findings indicate that the learning media is valid based on the analyzed validation sheets. Furthermore, the learning media is considered practical based on student response questionnaires, with an average score of 83.3%. The learning media also has a potential effect on conceptual understanding, as evidenced by the overall test results falling into the good category with an average score of 74.75%. Therefore, problem-solving-based digital learning media becomes an effective tool to assist students in developing their conceptual understanding in the process of learning flat-sided 3D spatial structures in geometry.

The Application of Frieze Groups and Crystallographic Groups in Generating Batak Toba Ornament Motifs Using a Matlab Graphical User Interface

Marlina Sinaga — 2024-01-19

Gorga is a carving or sculpture typically found on the exterior of a Toba Batak traditional house. The Batak people use fractal (geometric) dimensions in Batak gorga carvings. In mathematics, repetitive and symmetrical patterns in planes that result from transformations are included in the plane symmetry groups. Ethnomathematics is a cultural approach to the concept of mathematics. A frieze group can be defined as a symmetrical group which arises from a unidirectional translation and subsequently generates a linear pattern that recurs exclusively in a single direction. There are seven different pattern types in the frieze groups. Meanwhile, crystallographic patterns are flat two-dimensional patterns that form a lattice. There are 17 crystallographic types of patterns with five different types of unit lattices. The purpose of this study is to generate motifs for Batak ornaments based on frieze groups and crystallographic groups using a Matlab Graphical User Interface (GUI). A total of 119 new motifs were generated based on seven types of patterns in the frieze groups, namely, F1,F2,F3,F4,F5,F6, and F7. Meanwhile, in the crystallographic groups, 153 new motifs were generated based on nine types of patterns, namely, p1,p2,pm,pg,cm,pmg,pmm,cmm, and pgg. To keep with trends, the new motifs generated can be used in everyday life as decorations or business symbols that are characteristic of the Toba Batak region.

Exploring Students Learning Difficulties in Linear Function: A Diagnosis of Grade 9

Sarah Inayah — 2024-01-19

The aim of this research is to determine students' learning difficulties in completing diagnostic tests on linear function material. In managing data, quantitative procedures are used with the aim of reducing data. After that the data is analyzed using inductive data analysis and the processed data will be presented in narrative form. So this type of research is qualitative research. The subjects in this research were class IX students at a junior high school in Cianjur. The instruments used in this research were documentation, tests and interviews. The conclusions of the research results obtained include the types of student difficulties in straight line equation material are (1) difficulties in algorithmic abilities including a lack of planning abilities (strategy knowledge) and in solving abilities (algorithmic knowledge) which are shown from incomplete answers or lack of steps , the lack of accuracy of students in working; (2) difficulties in using the principle of linear functions, lack of mastery of the basics of algebra and lack of understanding (schematic knowledge) as indicated by difficulties in recognizing linear functions in contextual problems, errors in algebraic computations, difficulty in determining the point through which the line passes, and difficulty in apply the principle of parallel or perpendicular gradients; and (3) difficulties in using the concept including the inability to remember the concept, the inability to deduce useful information from a concept and the lack of understanding skills (schematic knowledge) which is shown by incompleteness in writing formulas. This research will be useful as a preliminary study in making learning designs to overcome student learning difficulties in linear function material based on empirical findings.

Sentiment Analysis Regarding Candidate Presidential 2024 Using Support Vector Machine Backpropagation Based

Atmaja Jalu Narendra Kisma — 2024-01-19

This research has the potential to make an important contribution to the development of computationally-based sentiment analysis, particularly in the political context. Anies Baswedan, Ganjar Pranowo, and Prabowo Subianto, three candidates for the presidency of Indonesia, are examined using a Backpropagation-based Support Vector Machine (SVM) methodology in this study. This approach is used to categorize emotions into three groups: neutral, adverse, and favorable. Between July 1 and July 30, 2023, data on tweets mentioning the three presidential contenders was gathered. After processing the data, SVM was used while lowering the backpropagation process. The study's findings demonstrate that the performance of the model in determining public sentiment is greatly enhanced by the application of backpropagation-based SVM techniques. For each presidential contender, the evaluation was conducted using the f1 score, recall, and precision metrics. The evaluation's findings indicate that while the model struggles to distinguish between favorable and negative feelings toward particular presidential contenders, it performs better when categorizing neutral feelings. The SVM model is more accurately able to identify popular sentiment toward the three presidential candidates when the backpropagation approach is used. The results of the sentiment analysis are also represented by word clouds for each presidential contender, giving an intuitive sense of the words that are frequently used in public discourse. This study sheds light on the possibilities of using Twitter data to analyze political sentiment using the backpropagation-based SVM algorithm.

Exploring Local Culture through Geometry Transformation: a Study of Banyumasan Batik

Ifada Novikasari — 2024-01-19

Banyumasan batik is one of Indonesia's cultural heritages from Banyumas Regency, which has unique and interesting patterns and motifs. This research paper describes the mathematical modelling of geometric transformations in Banyumasan batik. Geometric transformation is a mathematical technique for changing the shape or position of an object on a plane. This is qualitative research with an ethnographic approach. Data is collected through observation, interviews, and documentations. The data obtained were analysed using content analysis to identify various Banyumasan batik motifs that can be transformed into geometric forms. This study describes the basic geometric transformations, namely translations in Sekar Tirta batik motif, reflections in Bawor Kembar batik motif, dilations in Kawung Jenggot batik motif, and rotations in Manggar Bawor batik motif which applied to Banyumasan batik motifs. The results of this study include geometric transformations of Banyumasan batik motifs which are expected to positively contribute to the development of Indonesian art and culture, especially in the field of batik, enrich insight and knowledge about the application of mathematics in everyday life, and can be used for mathematical modelling and mathematics education based on local culture.

Employee Benefits Program Valuation with Multiple Decrement Model Based on PSAK 24 Post-COVID-19 Pandemic

Wahyuni Ekasasmita — 2024-01-19

In this article, we evaluate the post-labor compensation program based on PSAK-24 in the new normal era of the COVID-19 pandemic. In order to create a table multiple decrements based on a single table decrement namely, death, withdrawal, total permanent disability, and retirement. In the new normal era of the COVID-19 pandemic, the benefits of death, death caused by COVID-19, withdrawal, total permanent disability, and retirement were then aggregated. The method used in this study is a quantitative method with a case study approach of COVID-19. The data used is secondary data on the number of COVID-19 positive cases in Indonesia from January 2021 to December 2022. In this study, an actuarial model, the Multiple Decrement Model, was applied to calculate the valuation of the post-labor compensation program based on PSAK-24 using five decrements as the cause of claims consisting of death, death cause of COVID-19, withdrawal, total permanent disability and retirement. The calculation results that can be seen that large annual net premiums multiple decrement cases that provide benefits according to the cause of failure getting bigger as that person gets older.

Exploring the Characteristics of Digital Pedagogy Model for Developing Computational Thinking in Mathematical Problem Solving

Vita Nova Anwar — 2024-01-19

Challenges in the 21st century are increasingly complex, technology is developing rapidly and competition is getting tougher. Therefore we need quality human resources that can keep up with and anticipate the times. The use of technology involves computational thinking (CT) skills which are closely related to the problem-solving process. The stages in computational thinking are part of mathematical thinking, meaning that learning mathematics can support students' CT skills. Through the development of digital pedagogical models in CT integrated mathematics learning, it can improve problem-solving skills. This research usesÂ design based implementation research with 4 phases including; preliminary research, prototyping, results, and design principle. The participants were 28 grade 8 junior high school students who took part in two rounds of experiment in direct CT activities and digital CT activities. In this paper, we present an iterative mathematical problem-solving process in the digital pedagogy model. The computational task, environment, tool and practices were iteratively improved over two rounds to incorporate CT effectively in mathematics. The results from CT environment demonstrated that direct CT activities are more effective than digital CT activities in mathematical problem-solving.Â Based on empirical research, we summarize the characteristic of the digital pedagogy model from computational tasks, computational environment and tools, and computational practices in mathematical problem solving.

Implementation of Inquiry Learning Model in Collaboration with PBL to Improve Student Understanding in Number Theory Course

Lia Budi Tristanti — 2024-01-19

The purpose of this study was to describe the presence or absence of the influence of the infusion learning model collaboration with Problem-Based Learning (PBL)Â to develop students' understanding of proof and mathematical argumentation in number theory courses. This research is an experimental study with a randomized control group pretest-posttest design, two groups namely the experimental group and the control group. The experimental group is the group that uses the infusion learning model in collaboration with PBL, while the control group is the group that uses conventional learning. The subjects of this study consisted of 40 students at a university in Jombang, Indonesia. Data collection techniques through observation sheets, proof understanding tests and observation sheets of students' mathematical argumentation abilities. The results of the research show that the significant difference between the average proof of understanding of students in the experimental group and the control group. The difference between the average proof of understanding in the experimental group and the average proof of understanding of students in the control group was 21.75. Furthermore, the significant difference between the average argumentation ability of students in the experimental group and the control group. The difference between the average argumentation ability of students in the experimental group and the average argumentation ability of students in the control group is 5.25. Therefore, the implementasion of infusion learning in collaboration with PBL is more effective than conventional learning models for developing students' ability to understand mathematical proof and argumentation. This learning model promotes the development of critical thinking skills, problem-solving, conceptual and different understanding needed to construct a formal proof, and strong and valid arguments.

Development of Differentiate Student Worksheets: an Efforts to Improve Student Argumentation Ability

Zuhadur Ra'is Ariyono Putra — 2024-01-19

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.

Advancing Computational Thinking in Mathematics Education: a Systematic Review of Indonesian Research Landscape

Edi Irawan — 2024-01-19

Computational Thinking (CT) has emerged as a crucial and foundational skill in the 21st century, capturing the attention of researchers across various domains, including mathematics education in Indonesia. This research identifies and analyzes trends, themes, focuses, and research findings on CT through mathematics learning in Indonesia. This Systematic Literature Review (SLR) adheres to the PRISMA guidelines, encompassing three stages: search, selection, and data analysis. The search process on the Scopus database, utilizing queries aligned with the research objectives, yielded 31 articles related to CT and mathematics education authored by Indonesian researchers. Subsequent selection involved criteria such as research focus, study type, document availability, and intervention differences, resulting in 14 articles. Data analysis employed Bibliometrix and NVivo 14 Plus software. The findings reveal a significant increase in research on CT in mathematics education from Indonesian researchers over the past two years, with an annual growth rate of 5.74%. This publication landscape involves contributions from 39 authors affiliated with 16 higher education institutions in Indonesia. Researchers have delved into diverse themes, including the analysis of CT skill achievement, the development of CT-oriented instructional models and media, and the creation of assessment tools to measure CT skills. These findings underscore the broad relevance of CT in the realm of mathematics education. As a burgeoning field of study, numerous aspects of CT remain open for further research, development, and exploration, especially those related to mathematics. To enhance the impact and implementation of Computational Thinking (CT) within the context of Indonesian education, future research may consider investigating innovative pedagogical approaches, assessing the long-term impact of CT interventions, and exploring the potential integration of CT across various educational levels.

Nonlinear Principal Component Analysis with Mixed Data Formative Indicator Models in Path Analysis

Rindu Hardianti — 2024-01-19

This research aims to obtain the main component score of the latent variable ability to pay, determine the strongest indicators forming the ability to pay on a mixed scale based on predetermined indicators, and model the ability to pay on time as mediated by fear of paying using path analysis. The data used is secondary data obtained through distributing questionnaires with a mixed data scale. The sampling technique used in the research was purposive sampling. The number of samples used in the research was 100 customers. The method used is nonlinear principal component analysis with path analysis modeling. The results of this research show that of the five indicators formed by the Principal Component, 74.8% of diversity or information is able to be stored, while 25.20% of diversity or other information is not stored (wasted). Credit term is the strongest indicator that forms the ability to pay variable. The variable ability to pay mortgage has a significant effect on payments by mediating the fear of being late in paying with a coefficient of determination of 73.63%.

Mental Comparison of Students Learning Abacus-Arithmetic and Not Learning Abacus-Arithmetic on Mathematics Material

Loso Judijanto — 2024-01-19

Students' mental mastery in elementary school mathematics lessons in Indonesia is weak, slow, inaccurate, and declining. Mastery problems among elementary school students who have studied mental abacus arithmetic were found to be low. This is an urgent matter to research because there is a gap between theory, expectations, and reality. The purpose of this research was to compare the ability to solve mathematical problems between students who studied abacus mental arithmetic and students who did not study abacus mental arithmetic. This research involved 70 students. Data collection techniques using instruments, the instruments used were the first-semester mathematics exam and mental arithmetic exam. Data analysis techniques using SPSS Version 25.0 statistics, namely the t-test, were used to compare the ability to solve mathematical problems between students who studied mental abacus-arithmetic and students who did not study mental abacus-arithmetic. Pearson correlation was used to determine the relationship between students' mental arithmetic learning achievement and their ability to solve mathematical problems. The results of the research showed that there was a significant difference (p<0.05) in learning achievement on symbolic mathematics questions and mental arithmetic achievement between students who studied mental abacus calculation and students who did not study mental abacus calculation. The minimum score of the group that studied mental abacus calculation was higher compared to the group that did not study mental abacus calculation. However, there was no significant difference (p<0.05) in mathematics learning achievement between students who studied mental abacus-arithmetic and students who did not study mental abacus-arithmetic.Â

Comparison of Mediation Effects on Interaction and Multigroup Approach in Structural Equation Modeling PLS in Case of Bank Mortgage

Ulfah Maisaroh — 2024-01-19

â€œStructural Equation Modeling is one of multivariate statistical method that used to explain multiple relationships between latent variables simultaneously to test a mediation model to conduct a formal test on mediation effects. Application PLS-SEM for exploratory research and theory development are increasing. Under certain conditions, the effect of exogenous variables on endogenous variable is also strengthened or weakened by moderating variable. In SEM, there are two approaches in analyzing moderation variables, namely the interaction method and the multigroup method. This article aims to compare the mediation effect on interaction approaches and multigroup approaches in Structural Equation Modeling. The data used is the case of timeliness of Bank X mortgage payments. In this article, statistical methods are evaluated to compare indirect effect between groups and examine indirect effect on each group. It was concluded that Collectability Status moderates the indirect relationship between Capital and the Timeliness of Payment through Willingness to Pay. Debtors with current collectability status more strongly effect the Timeliness of Payment than debtors with incurrect collectability status. Theresults of testing indirect effects on moderation with interaction and multigroup approaches are not much different. In the multigroup approach, the bootstrap interval bias is smaller than the bootstrap interval bias in the interaction approach. The Q-square Predictive Relevance value in both methods is quite high, indicating that the model is good. On the Current Collectibility Status group Q^2 is 89.3%, in the incurrect Collectibility Status Q^2 is 84.2%. While in the interaction approach, Q^2 is 70.4%. Researcher recommend a multigroup approach to data that has categorical moderation variables because differences between groups can be directly observed without adding interaction variables in the model.â€

Platelet Modeling in DHF Patients Using Local Polynomial Semiparametric Regression on Longitudinal Data

Tiani Wahyu Utami — 2024-01-19

Regression analysis is one of the statistical methods used to model the relationship between response variables and predictor variables. Semiparametric regression is a combination of parametric and nonparametric regression. The estimator used in estimating the semiparametric regression model in this research is the Local Polynomial. Longitudinal data can be found in the health sector, including dengue hemorrhagic fever (DHF) data. The laboratory criteria for indication of DHF is thrombocytopenia. This research aims to obtain platelets model for DHF patients that can be used for forecasting so that it is hoped that it can provide information to the medical team in treating DHF patients. The estimated model used is Local Polynomial semiparametric regression on longitudinal data. The response variables in this research were platelets of DHF patients, which were influenced by hemoglobin as parametric predictor variable and examination time while hospitalized as nonparametric predictor variable. In the local polynomial regression model, it is necessary to select the optimal bandwidth and polynomial order method, GCV. The optimum bandwidth selection based on the GCV method obtained is 1.5 and polynomial order of 2, then applied to DHF patient platelet data, producing an estimated local polynomial semiparametric regression model that follows the actual data pattern. Modeling the platelets of DHF patients obtained using a local polynomial estimator resulted in an R2 value of 84.25% and MAPE of 4.5%, indicating highly accurate forecasting, so it can be concluded that the resulting model is better at predicting.

Determining the Inverse of a Matrix over Min-Plus Algebra

Siswanto Siswanto — 2024-01-19

Linear algebra over the semiringÂ R_Îµ with âŠ— (plus) and â¨ (maximum) operations which is known as max-plus algebra. One of the isomorphic with this algebra is a min-plus algebra. Min-plus algebra that is the set R_(Îµ^' )=Râˆª{Îµ'}, with âŠ—^' (plus) and â¨' (minimum) operations. Given a matrix whose components are elements of R_(Îµ^' )Â is called min-plus algebra matrices. Any matrix can be connected by an inverse. In conventional algebra, a square matrix is said an invertible matrix if the detâ¡ã€–(A)ã€—â‰ 0. In contrast to max-plus algebra, a matrix is said to have inverse condition if it meets certain conditions. Some concepts from the max-plus algebra can be transformed to the min-plus, because of their structural similarity. This means that the inverse matrix concept in max-plus can be constructed into a min-plus version. Thus, this study will explain the inverse of a matrix over the min-plus algebra, property of multiplying two invertible matrices, and connection between invertible matrix and linear mapping used the literature study method, with literature sources such as books, journals, articles, and theses. The data analysis technique used in this research is qualitative data analysis technique. Then, this article has a principal result that is matrix AâˆˆR_(Îµ^')^(nÃ—n) has a right inverse if and only if there are permutations of Ïƒ and the value of Î»_i<Îµ', iâˆˆ{1,2,3,â€¦,n} such that A=P_Ïƒ âŠ—^' D(Î»_i ) which is the inverse of matrices. Furthermore, if B is the correct inverse that satisfies AâŠ—^' B=E then BâŠ—^' A=E and B is uniquely determined by A.

ARIMA Time Series Modeling with the Addition of Intervention and Outlier Factors on Inflation Rate in Indonesia

Dewi Setyo Utami — 2024-01-19

Extreme events in a time series model can be detected when the precise timing of the event, known as the intervention, is known. When the exact timing of an event is unknown, it is referred to as an outlier.Â If these factors are neglected, the model's accuracy will be affected. To overcome this situation, it is possible to add the intervention or outlier factor into the time series model. This study proposes the combination of intervention and outlier analysis in time series models, especially ARIMA. It is intended to minimize the residuals and increase the accuracy of the model so that it is suitable for forecasting. Using the data of inflation rate in Indonesia, the conflict between Russia and Ukraine was used as an intervention factor in this case. Pre-intervention data (before February 2022) is used to construct the ARIMA model (1stÂ model). After that, the modeling process continued by adding the intervention factor to the ARIMA model. The effect caused by the intervention allows an outlier to appear, so the process is continued by adding the outlier factor, called an additive outlier, into the model before (2nd model). The MAPE for the first and second models is 7.96% and 7.57%, respectively. The finding of this research shows that the ARIMA model with intervention and outlier factors, named as the 2nd model, is the best model. This study shows that combining the intervention and outlier factors into ARIMA model can improve the accuracy. The forecasting of the inflation rate in Indonesia for one period ahead in 2023 is in the range of 2.06%.

Digital Media Innovation Based on Multimedia Cognitive and Constructivist Theory in a Cultural Context: Encouraging Students' Higher Order Thinking Skills

Budi Halomoan Siregar — 2024-01-19

The high-order thinking skills of students in Indonesia are classified as low, this is in line with the results of diagnostic tests conducted in class IX junior high school. Thus, it is necessary to develop digital media based on multimedia and constructivist cognitive theory with cultural context as one of the alternative solution. This study aims to (1) develop digital learning media based on constructivist and cognitive multimedia theories with a cultural context that fulfills the categories of validity, practicality and effectiveness; and (2) improve students' high-order thinking skills after using these media in the learning process. The research subjects were 30 students in class IX junior high school and the research objects were digital learning media based on constructivist theory and cognitive multimedia with a cultural context to improve students' high-level thinking skills on the topic of dilation. This is a research design with the Plomp model, which consists of (1) Preliminary research; (2) Prototyping phase; and (3) Assessment phase. The research instruments used were interviews, questionnaires and tests. The results showed that the product developed was included in the very valid, very practical, and effective category, where: (a) classical learning completeness reached 97%; (b) positive response by product users reached 97%; and (c) the N-Gain value was 0.791 in the very high category. Thus, it can be stated that the product meets the quality standard criteria, where the product can be used to improve students' high-level thinking abilities.

Matric Flux Potential in Time Independent Infiltration Problems from a Single Triangular and a Trapezoidal Irrigation Channel

Munadi Munadi — 2024-01-19

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.

Determination of Optimal Portfolio by Calculating Transaction Costs using Genetic Algorithms on the Jakarta Islamic Index

Sinta Oktavia Nur Fadhila — 2024-01-19

The optimal portfolio is a portfolio that can provide maximum returns at the same level of risk. In investing, the term "high return, high risk" is known, meaning that the higher the return, the higher the risk. Therefore, investors need to develop an optimal portfolio to obtain the maximum return on investment at the same level of risk. This study aims to determine the optimal formation of a stock portfolio by calculating transaction costs using the genetic algorithm method on stocks that are members of the Jakarta Islamic Index. This research uses data of daily return on stocks included in Jakarta Islamic Index from 1 August 2020-1 August 2022. The dataset consists of two variables: the date of observation and daily stock returns. The method used in this study is the minimum variance method and the genetic algorithm. Data analysis was divided into two stages: model formulation and model testing through case studies. The analysis of optimal portfolio formation using genetic algorithms shows that in terms of performance, the minimum variance portfolio is superior to the genetic algorithm portfolio, as indicated by the Sharpe ratio value. Meanwhile, the genetic algorithm portfolio is superior to the minimum variance portfolio regarding transaction costs. The genetic algorithm portfolio can provide a fairly high total return, small transaction costs, and good performance compared to the minimum portfolio. Hence, the genetic algorithm portfolio is worthy of recommendation to investors.

Control Chart for Correcting the ARIMA Time Series Model of GDP Growth Cases

Nurfitri Imro'ah — 2024-01-19

The essential prerequisite for attending the G20 conference is a country's GDP because G20 members can significantly boost the economy and preserve the nation's financial stability. Time series data can be thought of as a country's Gross Domestic Product (GDP) at a particular point in time. In this research, the GDP numbers from five Southeast Asian nations that are attending the G20 fulfilling are used. The total was 47 observations made yearly, which extended from 1975 to 2001. A time series analysis was performed on the data gathered. The correctness of time series models is also evaluated using control charts based on this research. The control chart is constructed using the time series model's residuals as observations. After applying the IMR control chart for verification, the results revealed that the residuals, specifically the models for GDP in Malaysia, Singapore, and Thailand, are out of control. The white noise assumption is fulfilled by the time series model obtained for Brunei and Indonesia's GDP, but the residuals are out of control. Whether controlled residuals are used depends on the accuracy with which the time series model predicts the future. If the amount of residuals is under control, then the time series model produced is accurate and good enough for prediction. After using the IMR control chart to verify the residuals, the results indicate that the residuals, namely the models for GDP in Malaysia, Singapore, and Thailand, are not under control. The assumption of white noise is proved correct by the time series model obtained for the GDP of Brunei Darussalam and Indonesia. With that being said, the residuals are entirely out of control. The model must improve its ability to forecast various future periods. It is a consequence of the unmanageable residuals that the model contains. Even if the best available model has been obtained based on the criteria that have been defined, it is anticipated that the research findings will improve the theories that have previously been developed and raise knowledge regarding the usefulness of testing the time series model. In addition to all of that, it is intended that the research will produce a summary of cases of an increase in GDP from five Southeast Asian countries participating in the G20 conference.