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All Journal GRADIEN Transcendent Journal of Mathematics and Applications
Hafnani Hafnani
Jurusan Matematika, FMIPA Universitas Syiah Kuala
Computer Science & IT Economics, Econometrics & Finance Environmental Science Mathematics Physics

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Prediksi Tingkat Kemiskinan di Provinsi Aceh dengan Model AR Munawar, Munawar; Hafnani, Hafnani
GRADIEN : Jurnal Ilmiah MIPA Vol 11, No 1 (2015): (Januari 2015)
Publisher : Universitas Bengkulu

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (216.543 KB)

Abstract

One indicator of the success of a government is the decreasing in the poverty rate. This paper aims to predict the percentage of poverty in the province of Aceh based on 9 years time series data, from 2005 up to 2013. The research method is autoregressive model . The data is secondary data obtained from Badan Pusat Statistik (BPS – Statistics Indonesia) of Aceh Province. The model obtained is . Based on the model  The prediction of the level of poverty in Aceh for 2014 is 18.27 percent of the total population of Aceh. This prediction has an error value of 0.22 and 1.29 respectively to the percentage of the poverty level in Aceh in March and September 2014. When viewed by urban and rural, the model  obtained is  and respectively for urban and rural. While the predictive value of the poverty level in Aceh in 2014 for urban areas is 11.73 percent and in rural areas is 20.81 percent.
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.
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.
Comparative Analysis of Joint Life Endowment Insurance Premium Reserves: Zillmer Method Versus Prospective Method and The Impact of Zillmer Level Hafnani, Hafnani; Maulidi, Ikhsan; Nurmaulidar, Nurmaulidar; Alindo, Sesda; Apriliani, Vina
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.v4i1.46121

Abstract

The insurance company collects premium reserves obtained from the difference between the value of benefits and the value of premium payments at a time of coverage. One method of premium reserve is prospective reserve, where the calculation is based on the difference between the present value of the benefits to be received and the present value of the net premiums that will come in accordance with a predetermined annuity. This research aims to determine the amount of premium and premium reserves in joint life endowment insurance using the Zillmer method which uses the concept of prospective reserves with gross premiums as the basis for calculations. Then we compare the result with premium reserves using prospective methods, and see the effect of the Zillmer level variable on the amount of premium reserves. The results of this study can be concluded that the value of joint life joint insurance premiums increases according to age when starting insurance and the reserves of joint life insurance premiums always increase every year, until at the end of the insurance coverage premium reserves will reach the same value as the amount of compensation. The value of the premium reserve is influenced by the value of the Zillmer level used; the greater the Zillmer level value, the greater the profit earned by the life insurance company.
Co-Authors Alindo, Sesda Damanik, Dieny Ahda Hanim, Safiatun Mahmudi Mahmudi Maulidi, Ikhsan Munawar Munawar Murida, Eva Nurmaulidar Nurmaulidar Pasaribu, Sri Rizki Aprilianti Radhiah, Radhiah Saiful Amri Siti Rusdiana Syafira, Nurul Vina Apriliani Yuni, Syarifah Meurah