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Journal : Transcendent Journal of Mathematics and Applications

Kesiklikan Grup Unit dari Ring Z_n Damanik, Dieny Ahda; Amri, Saiful; Hafnani, Hafnani
Transcendent Journal of Mathematics and Applications Vol 2, No 2 (2023)
Publisher : Syiah Kuala University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24815/tjoma.v2i2.35384

Abstract

The unit group of rings Z_n denoted by U_n is widely used in pure mathematics and applied mathematics. It makes the mathematics calculation in U_n more complicated as n gets bigger. However, when U_n is cyclic, the calculation is no longer matter. In previous research, it was shown that U_n is cyclic if and only if n = 2;4; p^k;2p^k for any odd prim p and any positive integer k. This statement is known as Gauss Theorem for primitive root. This paper aims to reprove The Gauss Theorem using various tools like divisibility in Z, group and ring, polynomials over integral domain and fields. It is stated by showing that U_ab is not cyclic where a,b 2, (a,b) = 1. Thus, the necessity for U_n to be cyclic, n must be of the form 2k; pk or 2pk. Furthermore, we find U_(2^k ) is cyclic if only if k {1,2}. And then, proved that U_p is cyclic and using induction on k, we find that U_(p^k ) is cyclic. Finally, it is also found that U_(2p^k ) is cyclic so that Gauss Theorem is proven.
Path Planning for Parking of Four Wheeled Vehicle with Minimum Energy and Optimum Parking Space Lutfan Milzam, Ahmad; Usman, Tarmizi; Ikhwan, Muhammad; Mahmudi, Mahmudi; Amri, Saiful
Transcendent Journal of Mathematics and Applications Vol 1, No 1 (2022)
Publisher : Syiah Kuala University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24815/tjoma.v1i1.28853

Abstract

As the number of private vehicles grows, so does the demand for parking space. It was also in charge of traffic congestion and high parking fees in downtown, particularly near public services and the central business district. The goal of this paper was to optimize path planning with the least amount of energy and the most parking space. To achieve this goal, three parts of optimization were used. They were divided into three categories: optimal parking space for obtaining area bounded and parking angle, path planning with boundaries and constraints to find the path with the least amount of energy, and finally vehicle direction for comparison with other recent works. The simulation revealed that the best parking space could result in a parking angle as the final vehicle direction. Based on the results, the produced path was more efficient, with an objective function energy of 394.44 unit of energy and a vehicle speed of 4.3 km/h. Because of its closeness to previous work, the route verified that it could be driven in reverse parking action.
Pengoptimalan Masalah Pemrograman Nonlinier menggunakan Metode Quadratic Programming Nurmaulidar, Nurmaulidar; Hafnani, Hafnani; Mahmudi, Mahmudi; Radhiah, Radhiah; Pasaribu, Sri Rizki Aprilianti; Amri, Saiful; Rusdiana, Siti
Transcendent Journal of Mathematics and Applications Vol 3, No 2 (2024)
Publisher : Syiah Kuala University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24815/tjoma.v3i2.43839

Abstract

Operations research is widely applied by industrial and business companies to maximize profits or minimize potential losses. In practice, many operations research problems cannot be solved using linear models and require nonlinear models instead. This is the case for Lavera Konveksi, a company that produces long-sleeve t-shirts, collared t-shirts, plain t-shirts, and training pants each month. The company faces issues with fluctuating production quantities and costs. This research aims to develop a nonlinear objective function model to minimize production costs and determine the minimum production cost and the optimal number of items to be produced by Lavera Konveksi. The data used in this study includes production quantities and costs for the period from December 2019 to April 2020. The research employs the Quadratic Programming method, where the nonlinear problem is transformed into a linear case and then solved using the Wolfe Simplex Method. The results indicate that Lavera Konveksi should produce 530 long-sleeve t-shirts, 455 collared t-shirts, 425 plain t-shirts, and 180 training pants to achieve a minimum production cost of IDR 49,436,799.
Prediction of the Population of Banda Aceh City Using the Laplace Transformation Syafira, Nurul; Murida, Eva; Hanim, Safiatun; Yuni, Syarifah Meurah; Amri, Saiful; Hafnani, Hafnani; Nurmaulidar, Nurmaulidar
Transcendent Journal of Mathematics and Applications Vol 3, No 1 (2024)
Publisher : Syiah Kuala University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24815/tjoma.v3i1.38764

Abstract

Population prediction is an estimate of the population in the future based on assumptions from the population growth rate. Based on data from the Central Statistics Agency (BPS), the population in Banda Aceh City is increasing every year with an average growth of around 2%. The purpose of this research is to predict the population in Banda Aceh City using the Laplace transformation on exponential model. The exponential model is a simple model to describe population growth patterns. Using Laplace transformation can easily get a difinitive analytic solution. The Laplace transformation of the exponential model is used to calculate the growth rate with data on the population of Banda Aceh City in 2015-2022. Based on the results of the study, the value of the growth rate (r) is obtained from determining the precentage error (MAPE) of each model to determine the predicted value that is closest to the actual value. So, model VII is the most accurate with a value (r) is 0,00412. The result of this study also show that model VII is used to predict the population in Banda Aceh City in 2030 when is 266.259 people.
Comparison Of Fuzzy Time Series Chen and Fuzzy Time Series Markov Chain Methods in Forecasting Consumer Price Index in Banda Aceh Syahrini, Intan; Tamimi, Afifah; Zuhra, Rahma; Amri, Saiful; Oktavia, Rini
Transcendent Journal of Mathematics and Applications Vol 4, No 1 (2025)
Publisher : Syiah Kuala University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24815/tjoma.v4i1.46243

Abstract

The Consumer Price Index (CPI) is utilized to determine a country's inflation and deflation rate. Inflation decreases the buying power of consumers; meanwhile, continuous deflation will lead to a recession. characterized by a stagnant economy and a diminished willingness among manufacturers to innovate. The CPI trends serve as a valuable economic indicator and a standard for manufacturing costs that reflect price fluctuations at the consumer level for specific goods and services. This study aims to forecast the CPI in Banda Aceh, Indonesia, utilizing CPI data in the region from January 2017 to October 2022 by applying the Fuzzy Time Series Chen and Fuzzy Time Series Markov Chain methods. Forecasting accuracy is assessed by the Mean Absolute Percentage Error (MAPE) and Mean Absolute Error (MAE). The Fuzzy Time Series Chen method obtained a MAPE of 2.98% and an MAE of 3.64, whereas the Fuzzy Time Series Markov Chain method attained a MAPE of 1.07% and an MAE of 1.27. This indicates that the predicting accuracy of the Fuzzy Time Series Markov Chain surpasses that of Chen's Fuzzy Time Series, leading to the conclusion that CPI forecasting in Banda Aceh City utilizing the Fuzzy Time Series Markov Chain approach is more precise.
Co-Authors Adrianda, Irsan Agus Pratama Agustiar Al Zuhri ambartiasari, Geta Anhar Fazri Anhar Fazri Arif Iskandar Armaini ' Armila Armila Asgha, Ashabul Yamin Asmaul Husna Aulia Rivaldi Baren, Maria Besri Nasrul Cut Asmaul Husna, Cut Asmaul Damanik, Dieny Ahda Darmawan Darmawan Desi Maulida Dewi Andriany Dimas Mandala PUTRA Fahmi Arfan Firman Fithroh Roshinah Roshinah Fitriliana Fitriliana Fitriliana Futri Syam Hafnani Hafnani hanifah hanifah Hanim, Safiatun Ira Damayanti Ismawati, Tri Jamalia, Jamalia Juwita Kasmaniar Kasmaniar Kasmaniar Laila Nursaliha lovita, Fantia Lutfan Milzam, Ahmad M Djamil Mahmudi Mahmudi Manovri Yeni Mariati Mariati MARIATI MARIATI Marlina Marlina Marlina Maulana Akbar, Rian Maulina Maulina, Maulina Mawaddarahmah, Mawaddarahmah Miftahurrahmah Miftahurrahmah, Miftahurrahmah Muhamad Ikbal Muhammad Ikhwan Mujiburrahman Mujiburrahman Mukhdasir Murida, Eva Muzakkir Nuzakkir Nurdin, Hanifah NURFARI Nurfiani Syamsuddin Nuril Fahdi, Nuril Nurmaulidar Nurmaulidar Nuzakkir, Muzakkir Oktavia, Rini Pasaribu, Sri Rizki Aprilianti Pratama, Agus Prayogo, Satrio Ajie Purnawan, Sastra Putri Mauliza, Putri Putri, Noni Radhiah, Radhiah RADHIANA RADHIANA, RADHIANA Rahma Zuhra Safitri, Yuni Ayu Saiful Samsul Ikhbar Samsul Ikhbar Sanjaya, Lilo Sarboini SARBOINI SARBOINI SARBOINI Sarboini Sarboini, Sarboini Sempena, Iwan Doa Siti Rusdiana Sudarman Sudarman Susanti Syafira, Nurul Syahrini, Intan Syamsuddin, Nurfiani Syamsul Rizal Syamsul Rizal Syamsul Rizal Tamimi, Afifah Taufik Hidayat Taufik Hidayat Usman, Tarmizi Wardani, Zakiatul Yuni, Syarifah Meurah Yusuf, Zulfan Zuhri, Al Zulfan Yusuf