Pub Date : 2024-01-19DOI: 10.31764/jtam.v8i1.17421
L. B. Tristanti, Toto Nusantara, Syarifatul Maf’ulah
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) 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.
{"title":"Implementation of Inquiry Learning Model in Collaboration with PBL to Improve Student Understanding in Number Theory Course","authors":"L. B. Tristanti, Toto Nusantara, Syarifatul Maf’ulah","doi":"10.31764/jtam.v8i1.17421","DOIUrl":"https://doi.org/10.31764/jtam.v8i1.17421","url":null,"abstract":"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) 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.","PeriodicalId":489521,"journal":{"name":"JTAM (Jurnal Teori dan Aplikasi Matematika)","volume":"80 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140503374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-19DOI: 10.31764/jtam.v8i1.16910
Etna Vianita
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. This 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. The models evaluated by average forecasting error rate (AFER) and compared with existing methods. AFER value 1.24% for proposed method.
{"title":"Ratio Interval-Frequency Density with Modifications to the Weighted Fuzzy Time Series","authors":"Etna Vianita","doi":"10.31764/jtam.v8i1.16910","DOIUrl":"https://doi.org/10.31764/jtam.v8i1.16910","url":null,"abstract":"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. This 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. The models evaluated by average forecasting error rate (AFER) and compared with existing methods. AFER value 1.24% for proposed method.","PeriodicalId":489521,"journal":{"name":"JTAM (Jurnal Teori dan Aplikasi Matematika)","volume":"95 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140502425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"Sentiment Analysis Regarding Candidate Presidential 2024 Using Support Vector Machine Backpropagation Based","authors":"Atmaja Jalu Narendra Kisma, Primandani Arsi, Pungkas Subarkah","doi":"10.31764/jtam.v8i1.17294","DOIUrl":"https://doi.org/10.31764/jtam.v8i1.17294","url":null,"abstract":"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. ","PeriodicalId":489521,"journal":{"name":"JTAM (Jurnal Teori dan Aplikasi Matematika)","volume":"486 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140502620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-19DOI: 10.31764/jtam.v8i1.17432
Siswanto Siswanto, A. Gusmizain
Linear algebra over the semiring R_ε with ⊗ (plus) and ⨁ (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_(ε^' )=R∪{ε'}, with ⊗^' (plus) and ⨁' (minimum) operations. Given a matrix whose components are elements of R_(ε^' ) 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 det〖(A)〗≠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 A∈R_(ε^')^(n×n) has a right inverse if and only if there are permutations of σ and the value of λ_i<ε', i∈{1,2,3,…,n} such that A=P_σ ⊗^' D(λ_i ) which is the inverse of matrices. Furthermore, if B is the correct inverse that satisfies A⊗^' B=E then B⊗^' A=E and B is uniquely determined by A.
{"title":"Determining the Inverse of a Matrix over Min-Plus Algebra","authors":"Siswanto Siswanto, A. Gusmizain","doi":"10.31764/jtam.v8i1.17432","DOIUrl":"https://doi.org/10.31764/jtam.v8i1.17432","url":null,"abstract":"Linear algebra over the semiring R_ε with ⊗ (plus) and ⨁ (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_(ε^' )=R∪{ε'}, with ⊗^' (plus) and ⨁' (minimum) operations. Given a matrix whose components are elements of R_(ε^' ) 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 det〖(A)〗≠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 A∈R_(ε^')^(n×n) has a right inverse if and only if there are permutations of σ and the value of λ_i<ε', i∈{1,2,3,…,n} such that A=P_σ ⊗^' D(λ_i ) which is the inverse of matrices. Furthermore, if B is the correct inverse that satisfies A⊗^' B=E then B⊗^' A=E and B is uniquely determined by A.","PeriodicalId":489521,"journal":{"name":"JTAM (Jurnal Teori dan Aplikasi Matematika)","volume":"451 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140502686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-19DOI: 10.31764/jtam.v8i1.16675
Prizka Rismawati Arum, Lisa Anggraini, Indah Manfaati Nur, Eko Andy Purnomo
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 2017─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.
{"title":"Panel Data Spatial Regression Modeling with a Rook Contiguity Weighting Function on the Human Development Index in West Sumatera Province","authors":"Prizka Rismawati Arum, Lisa Anggraini, Indah Manfaati Nur, Eko Andy Purnomo","doi":"10.31764/jtam.v8i1.16675","DOIUrl":"https://doi.org/10.31764/jtam.v8i1.16675","url":null,"abstract":"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 2017─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. ","PeriodicalId":489521,"journal":{"name":"JTAM (Jurnal Teori dan Aplikasi Matematika)","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140503361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-19DOI: 10.31764/jtam.v8i1.17417
Wahyuni Ekasasmita, Nur Rahmi, M. F. Iskandar
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.
{"title":"Employee Benefits Program Valuation with Multiple Decrement Model Based on PSAK 24 Post-COVID-19 Pandemic","authors":"Wahyuni Ekasasmita, Nur Rahmi, M. F. Iskandar","doi":"10.31764/jtam.v8i1.17417","DOIUrl":"https://doi.org/10.31764/jtam.v8i1.17417","url":null,"abstract":"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. ","PeriodicalId":489521,"journal":{"name":"JTAM (Jurnal Teori dan Aplikasi Matematika)","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140503518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-19DOI: 10.31764/jtam.v8i1.16917
S. Maryani, Dede Bagus Suhada, Bambang Hendriya Guswanto
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 Weis’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).
{"title":"Partial Fourier Transform Method for Solution Formula of Stokes Equation with Robin Boundary Condition in Half-space","authors":"S. Maryani, Dede Bagus Suhada, Bambang Hendriya Guswanto","doi":"10.31764/jtam.v8i1.16917","DOIUrl":"https://doi.org/10.31764/jtam.v8i1.16917","url":null,"abstract":"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 Weis’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).","PeriodicalId":489521,"journal":{"name":"JTAM (Jurnal Teori dan Aplikasi Matematika)","volume":"59 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140502797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-19DOI: 10.31764/jtam.v8i1.17469
Sinta Oktavia Nur Fadhila, Agus Maman Abadi, Ezra Putranda Setiawan
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.
{"title":"Determination of Optimal Portfolio by Calculating Transaction Costs using Genetic Algorithms on the Jakarta Islamic Index","authors":"Sinta Oktavia Nur Fadhila, Agus Maman Abadi, Ezra Putranda Setiawan","doi":"10.31764/jtam.v8i1.17469","DOIUrl":"https://doi.org/10.31764/jtam.v8i1.17469","url":null,"abstract":"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.","PeriodicalId":489521,"journal":{"name":"JTAM (Jurnal Teori dan Aplikasi Matematika)","volume":"57 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140502899","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-19DOI: 10.31764/jtam.v8i1.17130
Marlina Sinaga, Dinda Kartika
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.
{"title":"The Application of Frieze Groups and Crystallographic Groups in Generating Batak Toba Ornament Motifs Using a Matlab Graphical User Interface","authors":"Marlina Sinaga, Dinda Kartika","doi":"10.31764/jtam.v8i1.17130","DOIUrl":"https://doi.org/10.31764/jtam.v8i1.17130","url":null,"abstract":"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.","PeriodicalId":489521,"journal":{"name":"JTAM (Jurnal Teori dan Aplikasi Matematika)","volume":"456 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140502665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-19DOI: 10.31764/jtam.v8i1.17033
Munadi Munadi, M. S. Rokhman, Dian Nataria Oktaviani, Ahmadi Ahmadi, Helmi Roichatul Jannah
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.
{"title":"Matric Flux Potential in Time Independent Infiltration Problems from a Single Triangular and a Trapezoidal Irrigation Channel","authors":"Munadi Munadi, M. S. Rokhman, Dian Nataria Oktaviani, Ahmadi Ahmadi, Helmi Roichatul Jannah","doi":"10.31764/jtam.v8i1.17033","DOIUrl":"https://doi.org/10.31764/jtam.v8i1.17033","url":null,"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. ","PeriodicalId":489521,"journal":{"name":"JTAM (Jurnal Teori dan Aplikasi Matematika)","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140503037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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