Pub Date : 2023-11-27DOI: 10.14710/jfma.v6i2.20750
A. Alridha
In this paper, we undertake an in-depth exploration of the optimization of parameters governing the trajectory of a projectile. Our primary objective is the determination of the optimal launch angle and initial velocity that yield the maximum achievable range for the projectile. To accomplish this, we leverage five distinct optimization methodologies, specifically the Nelder-Mead, Powell, L-BFGS-B, TNC, and SLSQP algorithms, in pursuit of our research goals. This paper offers a comprehensive analysis of the optimization procedures, shedding light on the impact of these diverse algorithms on the resultant outcomes. For each set of optimized parameters, the manuscript conducts extensive simulations of the projectile’s trajectory, presenting visual depictions of the paths traversed by the projectile. Additionally, our study incorporates comparative charts to emphasize the performance distinctions among various algorithms with respect to both maximum range and launch angle.
{"title":"OPTIMIZATION ALGORITHMS FOR PROJECTILE MOTION: MAXIMIZING RANGE AND DETERMINING OPTIMAL LAUNCH ANGLE","authors":"A. Alridha","doi":"10.14710/jfma.v6i2.20750","DOIUrl":"https://doi.org/10.14710/jfma.v6i2.20750","url":null,"abstract":"In this paper, we undertake an in-depth exploration of the optimization of parameters governing the trajectory of a projectile. Our primary objective is the determination of the optimal launch angle and initial velocity that yield the maximum achievable range for the projectile. To accomplish this, we leverage five distinct optimization methodologies, specifically the Nelder-Mead, Powell, L-BFGS-B, TNC, and SLSQP algorithms, in pursuit of our research goals. This paper offers a comprehensive analysis of the optimization procedures, shedding light on the impact of these diverse algorithms on the resultant outcomes. For each set of optimized parameters, the manuscript conducts extensive simulations of the projectile’s trajectory, presenting visual depictions of the paths traversed by the projectile. Additionally, our study incorporates comparative charts to emphasize the performance distinctions among various algorithms with respect to both maximum range and launch angle.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"120 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139232112","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 : 2023-11-27DOI: 10.14710/jfma.v6i2.20091
Muhammad Manaqib, Ayu Kinasih Yuliawati, Dhea Urfina Zulkifli
This study developed a model for the spread of measles based on the SEIR model by adding the factors of using the first dose of vaccination, the second dose of vaccination, and treatment. Making this model begins with making a compartment diagram of the spread of the disease, which consists of seven subpopulations, namely susceptible subpopulations, subpopulations that have received the first dose of vaccination, subpopulations that have received the second dose vaccination, exposed subpopulations, infected subpopulations, subpopulations that have received treatment, and subpopulations healed. After the model is formed, the disease-free equilibrium point, endemic equilibrium point, and basic reproduction number (R_0) are obtained. Analysis of the stability of the disease-for equilibrium point was locally asymptotically stable when (R_0)<1. The backward bifurcation analysis occurs when (R_C) is present and R_C
{"title":"MATHEMATICAL MODEL OF MEASLES DISEASE SPREAD WITH TWO-DOSE VACCINATION AND TREATMENT","authors":"Muhammad Manaqib, Ayu Kinasih Yuliawati, Dhea Urfina Zulkifli","doi":"10.14710/jfma.v6i2.20091","DOIUrl":"https://doi.org/10.14710/jfma.v6i2.20091","url":null,"abstract":"This study developed a model for the spread of measles based on the SEIR model by adding the factors of using the first dose of vaccination, the second dose of vaccination, and treatment. Making this model begins with making a compartment diagram of the spread of the disease, which consists of seven subpopulations, namely susceptible subpopulations, subpopulations that have received the first dose of vaccination, subpopulations that have received the second dose vaccination, exposed subpopulations, infected subpopulations, subpopulations that have received treatment, and subpopulations healed. After the model is formed, the disease-free equilibrium point, endemic equilibrium point, and basic reproduction number (R_0) are obtained. Analysis of the stability of the disease-for equilibrium point was locally asymptotically stable when (R_0)<1. The backward bifurcation analysis occurs when (R_C) is present and R_C<R_0. Numerical simulations of disease-free and endemic equilibrium points are carried out to provide an overview of the results analyzed with parameter values from several sources. The results of the numerical simulation are in line with the analysis carried out. From the model analysis, the disease will disappear more quickly when the level of vaccine used and individuals who carry out treatment are enlarged.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139229727","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 : 2023-11-27DOI: 10.14710/jfma.v6i2.20150
Sulma Sulma, Nur Ahniyanti Rasyid, I. N. Widana
Civil servants have an important role in national development, so increasing their productivity is needed. The pension fund program is given as a form of effort by government agencies to ensure employee welfare when entering retirement. This research discusses the normal cost of the defined benefit pension program using one of the actuarial valuation methods, namely Frozen Initial Liability (FIL), by taking into account the stochastic interest rate following the Vasicek model. The data used in this study are lecturers majoring in MIPA, Faculty of Science and Technology, Universitas Jambi, consisting of 8 people of female gender with the status of being a participant since 2022. Based on the calculation results obtained that in the period 0-30 years, the normal cost for each group member is constant, namely per year or per month. When the working period entered 31 years, one by one the participants began to enter their retirement period, which resulted in a change in the normal cost value. At 38 years of service, there was only one participant with a normal cost of per year or by per month. Changes in normal cost tend to decrease when retirement program participants also decrease. In the period of more than 38 years, all participants have retired so that normal cost payments are stopped.
{"title":"FROZEN INITIAL LIABILITY METHOD TO DETERMINE NORMAL COST OF PENSION FUND WITH VASICEK INTEREST RATE MODEL","authors":"Sulma Sulma, Nur Ahniyanti Rasyid, I. N. Widana","doi":"10.14710/jfma.v6i2.20150","DOIUrl":"https://doi.org/10.14710/jfma.v6i2.20150","url":null,"abstract":"Civil servants have an important role in national development, so increasing their productivity is needed. The pension fund program is given as a form of effort by government agencies to ensure employee welfare when entering retirement. This research discusses the normal cost of the defined benefit pension program using one of the actuarial valuation methods, namely Frozen Initial Liability (FIL), by taking into account the stochastic interest rate following the Vasicek model. The data used in this study are lecturers majoring in MIPA, Faculty of Science and Technology, Universitas Jambi, consisting of 8 people of female gender with the status of being a participant since 2022. Based on the calculation results obtained that in the period 0-30 years, the normal cost for each group member is constant, namely per year or per month. When the working period entered 31 years, one by one the participants began to enter their retirement period, which resulted in a change in the normal cost value. At 38 years of service, there was only one participant with a normal cost of per year or by per month. Changes in normal cost tend to decrease when retirement program participants also decrease. In the period of more than 38 years, all participants have retired so that normal cost payments are stopped.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139229771","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 : 2023-11-27DOI: 10.14710/jfma.v6i2.20084
Muchamad Harry Yudha Pratama, Agus Yodi Gunawan
In this paper, we explore a cutting-edge technique called as Physics- Informed Neural Networks (PINN) to tackle boundary layer problems. We here examine four different cases of boundary layers of second-order ODE: a linear ODEwith constant coefficients, a nonlinear ODE with homogeneous boundary conditions, an ODE with non-constant coefficients, and an ODE featuring multiple boundary layers. We adapt the line of PINN technique for handling those problems, and our results show that the accuracy of the resulted solutions depends on how we choose the most reliable and robust activation functions when designing the architecture of the PINN. Beside that, through our explorations, we aim to improve our understanding on how the PINN technique works better for boundary layer problems. Especially, the use of the SiLU (Sigmoid-Weighted Linear Unit) activation function in PINN has proven to be particularly remarkable in handling our boundary layer problems.
{"title":"EXPLORING PHYSICS-INFORMED NEURAL NETWORKS FOR SOLVING BOUNDARY LAYER PROBLEMS","authors":"Muchamad Harry Yudha Pratama, Agus Yodi Gunawan","doi":"10.14710/jfma.v6i2.20084","DOIUrl":"https://doi.org/10.14710/jfma.v6i2.20084","url":null,"abstract":"In this paper, we explore a cutting-edge technique called as Physics- Informed Neural Networks (PINN) to tackle boundary layer problems. We here examine four different cases of boundary layers of second-order ODE: a linear ODEwith constant coefficients, a nonlinear ODE with homogeneous boundary conditions, an ODE with non-constant coefficients, and an ODE featuring multiple boundary layers. We adapt the line of PINN technique for handling those problems, and our results show that the accuracy of the resulted solutions depends on how we choose the most reliable and robust activation functions when designing the architecture of the PINN. Beside that, through our explorations, we aim to improve our understanding on how the PINN technique works better for boundary layer problems. Especially, the use of the SiLU (Sigmoid-Weighted Linear Unit) activation function in PINN has proven to be particularly remarkable in handling our boundary layer problems.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139233456","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 : 2023-11-27DOI: 10.14710/jfma.v6i2.18996
Yuli Sri Afrianti, Fadhil Hanif Sulaiman, Sandy Vantika
. Flower Pollination Algorithm (FPA) is an optimization method that adopts the way flower pollination works by selecting switch probabilities to determine the global or local optimization process. The choice of switch probability value will influence the number of iterations required to reach the optimum value. In several previous literatures, the switch probability value was always chosen as 0.8 because naturally the global probability is greater than local. In this article, comparison is studied to determine the switch probability by using the Double Exponent rule. The results are analyzed using Hypothesis Testing to test whether there is a significant difference between the optimization results. The study involved ten testing functions, and results showed that the 0.8 treatment is significantly different from the Double Exponent. However, in general no treatment is better than the other.
{"title":"FLOWER POLLINATION ALGORITHM (FPA): COMPARING SWITCH PROBABILITY BETWEEN CONSTANT 0.8 AND DOUBLE EXPONENTGUNAKAN DOUBLE EXPONENT","authors":"Yuli Sri Afrianti, Fadhil Hanif Sulaiman, Sandy Vantika","doi":"10.14710/jfma.v6i2.18996","DOIUrl":"https://doi.org/10.14710/jfma.v6i2.18996","url":null,"abstract":". Flower Pollination Algorithm (FPA) is an optimization method that adopts the way flower pollination works by selecting switch probabilities to determine the global or local optimization process. The choice of switch probability value will influence the number of iterations required to reach the optimum value. In several previous literatures, the switch probability value was always chosen as 0.8 because naturally the global probability is greater than local. In this article, comparison is studied to determine the switch probability by using the Double Exponent rule. The results are analyzed using Hypothesis Testing to test whether there is a significant difference between the optimization results. The study involved ten testing functions, and results showed that the 0.8 treatment is significantly different from the Double Exponent. However, in general no treatment is better than the other.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139231390","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 : 2023-11-27DOI: 10.14710/jfma.v6i2.18504
Klatenia Selawati, Christiana Rini Indrati
. In this paper, we will discuss about topological properties of quasi-pseudometric spaces and properties of linear operators in asymmetric normed spaces. The topological properties of quasi-pseudometric spaces will be given consisting of open and closed set properties in quasi-pseudometric spaces. The discussion about properties of linear operator on asymmetric normed spaces is focus on the uniform boundedness principle. The uniform boundedness theorem is proved by utilizing completeness properties and characteristic of closed sets on quasi-pseudometric spaces.
{"title":"TOPOLOGY OF QUASI-PSEUDOMETRIC SPACES AND CONTINUOUS LINEAR OPERATOR ON ASYMMETRIC NORMED SPACES","authors":"Klatenia Selawati, Christiana Rini Indrati","doi":"10.14710/jfma.v6i2.18504","DOIUrl":"https://doi.org/10.14710/jfma.v6i2.18504","url":null,"abstract":". In this paper, we will discuss about topological properties of quasi-pseudometric spaces and properties of linear operators in asymmetric normed spaces. The topological properties of quasi-pseudometric spaces will be given consisting of open and closed set properties in quasi-pseudometric spaces. The discussion about properties of linear operator on asymmetric normed spaces is focus on the uniform boundedness principle. The uniform boundedness theorem is proved by utilizing completeness properties and characteristic of closed sets on quasi-pseudometric spaces.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"357 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139230683","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 : 2023-11-27DOI: 10.14710/jfma.v6i2.19307
Muchammad Choerul Arifin, Iwan Ernanto
An idempotent element in the algebraic structure of a ring is an element that, when multiplied by itself, yields an outcome that remains unchanged and identical to the original element. Any ring with a unity element generally has two idempotent elements, 0 and 1, these particular idempotent elements are commonly referred to as the trivial idempotent elements However, in the case of rings $mathbb{Z}_n$ and $mathbb{Z}_n[x]$ it is possible to have non-trivial idempotent elements. In this paper, we will investigate the idempotent elements in the polynomial ring $mathbb{Z}_{p^2q}[x]$ with $p,q$ different primes. Furthermore, the form and characteristics of non-trivial idempotent elements in $M_2(mathbb{Z}_{p^2q}[x])$ will be investigated. The results showed that there are 4 idempotent elements in $mathbb{Z}_{p^2q}[x]$ and 7 idempotent elements in $M_2(mathbb{Z}_{p^2q}[x])$.
{"title":"IDEMPOTENT ELEMENTS IN MATRIX RING OF ORDER 2 OVER POLYNOMIAL RING $mathbb{Z}_{p^2q}[x]$","authors":"Muchammad Choerul Arifin, Iwan Ernanto","doi":"10.14710/jfma.v6i2.19307","DOIUrl":"https://doi.org/10.14710/jfma.v6i2.19307","url":null,"abstract":"An idempotent element in the algebraic structure of a ring is an element that, when multiplied by itself, yields an outcome that remains unchanged and identical to the original element. Any ring with a unity element generally has two idempotent elements, 0 and 1, these particular idempotent elements are commonly referred to as the trivial idempotent elements However, in the case of rings $mathbb{Z}_n$ and $mathbb{Z}_n[x]$ it is possible to have non-trivial idempotent elements. In this paper, we will investigate the idempotent elements in the polynomial ring $mathbb{Z}_{p^2q}[x]$ with $p,q$ different primes. Furthermore, the form and characteristics of non-trivial idempotent elements in $M_2(mathbb{Z}_{p^2q}[x])$ will be investigated. The results showed that there are 4 idempotent elements in $mathbb{Z}_{p^2q}[x]$ and 7 idempotent elements in $M_2(mathbb{Z}_{p^2q}[x])$.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"55 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139234797","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 : 2023-11-27DOI: 10.14710/jfma.v6i2.18155
Joshua Erlangga Sakti, Muhammad Arzaki, G. S. Wulandari
We study algorithmic aspects of the Path puzzle--a logic puzzle created in 2013 and confirmed NP-complete (Non-deterministic Polynomial-time-complete) in 2020. We propose a polynomial time algorithm for verifying an arbitrary Path puzzle solution and a backtracking-based method for finding a solution to an arbitrary Path puzzle instance.To our knowledge, our study is the first rigorous investigation of an imperative algorithmic approach for solving Path puzzles. We prove that the asymptotic running time of our proposed method in solving an arbitrary Path puzzle instance of size $m times n$ is $O(3^{mn})$. Despite this exponential upper bound, experimental results imply that a C++ implementation of our algorithm can quickly solve $6 times 6$ Path puzzle instances in less than 30 milliseconds with an average of 3.02 milliseconds for 26 test cases. We finally prove that an $m times n$ Path puzzle instance without row and column constraints is polynomially solvable in $O(max{m,n})$ time.
我们研究了 "路径谜题 "的算法问题。"路径谜题 "是2013年提出的一个逻辑谜题，2020年被确认为NP完备（非确定性多项式时间完备）。我们提出了一种验证任意路径谜题解的多项式时间算法，以及一种为任意路径谜题实例寻找解的基于回溯的方法。据我们所知，我们的研究是对解决路径谜题的命令式算法方法的首次严格研究。我们证明，在解决大小为 $m times n$ 的任意路径谜题实例时，我们提出的方法的渐进运行时间为 $O(3^{mn})$。尽管存在这个指数级上限，但实验结果表明，我们算法的C++实现可以在30毫秒内快速解决大小为 $6 times 6$ 的路径谜题实例，26个测试案例的平均时间为3.02毫秒。最后，我们证明了一个没有行列约束的 $m times n$ 路径谜题实例可以在 $O(max{m,n})$ 时间内多项式求解。
{"title":"A BACKTRACKING APPROACH FOR SOLVING PATH PUZZLES","authors":"Joshua Erlangga Sakti, Muhammad Arzaki, G. S. Wulandari","doi":"10.14710/jfma.v6i2.18155","DOIUrl":"https://doi.org/10.14710/jfma.v6i2.18155","url":null,"abstract":"We study algorithmic aspects of the Path puzzle--a logic puzzle created in 2013 and confirmed NP-complete (Non-deterministic Polynomial-time-complete) in 2020. We propose a polynomial time algorithm for verifying an arbitrary Path puzzle solution and a backtracking-based method for finding a solution to an arbitrary Path puzzle instance.To our knowledge, our study is the first rigorous investigation of an imperative algorithmic approach for solving Path puzzles. We prove that the asymptotic running time of our proposed method in solving an arbitrary Path puzzle instance of size $m times n$ is $O(3^{mn})$. Despite this exponential upper bound, experimental results imply that a C++ implementation of our algorithm can quickly solve $6 times 6$ Path puzzle instances in less than 30 milliseconds with an average of 3.02 milliseconds for 26 test cases. We finally prove that an $m times n$ Path puzzle instance without row and column constraints is polynomially solvable in $O(max{m,n})$ time.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"102 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139229563","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 : 2023-07-02DOI: 10.14710/jfma.v6i1.16468
Naura Ghina As-shofa, Vemmie Nastiti Lestari
. K-medoids is one of the partitioning methods with the medoid as its center cluster, where medoid is the most centrally located object in a cluster, which is robust to outliers. The k-medoids algorithm used in this study is Clustering Large Application Using Metaheuristics (CLAM), where CLAM is a development of the Clustering Large Application based on Randomized Search (CLARANS) algorithm in improving the quality of cluster analysis by using hybrid metaheuristics between Tabu Search (TS) and Variable Neighborhood Search (VNS). In the case study, the best cluster analysis method for classifying sub-districts on the island of Sumatra based on elementary school availability and elementary school process standards is the CLAM method with k=6, num local = 2, max neighbor = 154, tls = 50 and set radius = 100-10:5. It can be seen that based on the overall average silhouette width value, the CLAM method is better than the CLARANS method.
{"title":"CLUSTERING LARGE APPLICATION USING METAHEURISTICS (CLAM) FOR GROUPING DISTRICTS BASED ON PRIMARY SCHOOL DATA ON THE ISLAND OF SUMATRA","authors":"Naura Ghina As-shofa, Vemmie Nastiti Lestari","doi":"10.14710/jfma.v6i1.16468","DOIUrl":"https://doi.org/10.14710/jfma.v6i1.16468","url":null,"abstract":". K-medoids is one of the partitioning methods with the medoid as its center cluster, where medoid is the most centrally located object in a cluster, which is robust to outliers. The k-medoids algorithm used in this study is Clustering Large Application Using Metaheuristics (CLAM), where CLAM is a development of the Clustering Large Application based on Randomized Search (CLARANS) algorithm in improving the quality of cluster analysis by using hybrid metaheuristics between Tabu Search (TS) and Variable Neighborhood Search (VNS). In the case study, the best cluster analysis method for classifying sub-districts on the island of Sumatra based on elementary school availability and elementary school process standards is the CLAM method with k=6, num local = 2, max neighbor = 154, tls = 50 and set radius = 100-10:5. It can be seen that based on the overall average silhouette width value, the CLAM method is better than the CLARANS method.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139364333","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 : 2023-07-02DOI: 10.14710/jfma.v6i1.15939
A. G. Syarifudin, Verrel Rievaldo Wijaya
The dihedral group of order 2n denoted by D_2n is the symmetry group of a regular -polygon consisting of rotation and reflection elements and the composition of both elements. Like any other group, the dihedral group also have a subgroup whose numbers differs depending on the value of n. This research is conducted by studying past literature and explore a new development to a theory. In this paper, all the form of proper subgroups of D_2n will be given and all of these proper subgroups of D_2n will be generated and counted with the help of Python program.
{"title":"A PYTHON CODE FOR GENERATING ALL PROPER SUBGROUPS OF DIHEDRAL GROUP","authors":"A. G. Syarifudin, Verrel Rievaldo Wijaya","doi":"10.14710/jfma.v6i1.15939","DOIUrl":"https://doi.org/10.14710/jfma.v6i1.15939","url":null,"abstract":"The dihedral group of order 2n denoted by D_2n is the symmetry group of a regular -polygon consisting of rotation and reflection elements and the composition of both elements. Like any other group, the dihedral group also have a subgroup whose numbers differs depending on the value of n. This research is conducted by studying past literature and explore a new development to a theory. In this paper, all the form of proper subgroups of D_2n will be given and all of these proper subgroups of D_2n will be generated and counted with the help of Python program.","PeriodicalId":359074,"journal":{"name":"Journal of Fundamental Mathematics and Applications (JFMA)","volume":"80 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139364335","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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