Diophantine Journal of Mathematics and Its Applications

Pemodelan Jumlah Pengguna Metode Kontrasepsi Jangka Panjang (MKJP) Di Provinsi Bengkulu Menggunakan Metode Arima dan Prophet

2024-12-07T02:13:05+00:00

The use of contraceptives, especially Long-Term Contraceptive Methods (MKJP), plays a central role in birth control efforts and family planning. Time series analysis has become a very effective method for identifying and predicting patterns in sequential data such as MKJP usage data. The data used is monthly data on the number of users of MKJP contraceptives (IUD, MOW, MOP and Implant) for the period January 2012 to 2012. December 2023. The aim of this research is to obtain comparative results of the accuracy of forecasting models using the Autoregressive Integrated Moving Average (ARIMA) and Prophet methods and to obtain projected results of MKJP contraceptive users in Bengkulu Province in the coming year. The results obtained overall, the ARIMA model is the best model for forecasting because it has mean absolute percentage error MAPE and root mean square error RMSE values, namely the ARIMA model (0,1,1). The forecast results for the number of MKJP contraceptive users (IUD, MOW, MOP and Implant) in 2024 tend to show a decreasing trend in May 2024 and an increasing trend in March 2024. For IUD contraception, it is known that the number of active family planning (PA) users is the lowest. was May 2024 with a total of 5593 participants, while the highest PA occurred in March 2024, namely 16742 participants. Then for MOW contraception, the lowest number of PAs was in May 2024, amounting to 6028 participants, while the highest PA was in March 2024, amounting to 8417 participants. Furthermore, for MOP contraception, it is known that the lowest number of PAs was in December 2024, amounting to 79 participants, while the peak PA occurred in March 2024, namely 614 participants. And finally, for IMPLANT contraception, it is known that the lowest number of PA was in May 2024, amounting to 26,771 participants, while the highest PA occurred in March 2024, namely 50,957 participants.

The Relation Between Bézout Domain, Elementary Divisor Domain, and Adequate Domain

2024-11-26T07:51:38+00:00

The aim of this paper is to investigate the relationship between Bézout domain, elementary divisor domain, and adequate domain. A Bézout domain is an integral domain D which every finitely generated ideal of D is principal. An integral domain D is called an elementary divisor domain if every matrix over D is equivalent to Smith normal form matrix. An adequate domain D is a Bézout domain and RP(a,b) exists for all a,b∈D with a≠0. Here the notion RP(a,b) defined as the relatively prime part of a with respect to b. It is found that every elementary divisor domain is a Bézout domain, but the converse is not true in general. It is shown the sufficient conditions for the Bézout domain being an elementary divisor domain. We also find out that every adequate domain is an elementary divisor domain. Furthermore, every one-dimensional Bézout domain is an adequate domain.

PERBANDINGAN ARIMA DAN FUZZY TIME SERIES MARKOV CHAIN UNTUK MERAMALKAN PREDIKSI HASIL PANEN KOPI (Studi kasus Kabupaten Bengkulu Tengah Tahun 2012-2022)

2023-12-27T05:49:32+00:00

Penelitian ini bertujuan untuk membandingkan metode ARIMA dan Fuzzy Time Series Markov Chain dalam meramalkan prediksi hasil panen kopi pada studi kasus Kabupaten Bengkulu Tengah tahun 2012-2022. Langkah-langkah yang dilakukan dalam penelitian ini meliputi pengumpulan data, analisis data, pemodelan data, uji model, evaluasi model, dan kesimpulan. Model ARIMA digunakan untuk memodelkan komponen linear dari data hasil panen kopi, sedangkan metode Fuzzy Time Series Markov Chain digunakan untuk memodelkan komponen non-linear. Uji model dilakukan dengan membandingkan hasil peramalan dari kedua model dengan data aktual. Evaluasi dilakukan dengan menggunakan metrik evaluasi seperti Mean Absolute Percentage Error (MAPE) dan Root Mean Square Error (RMSE). Berdasarkan hasil penelitian, diperoleh kesimpulan bahwa model ARIMA memberikan hasil peramalan yang lebih baik dibandingkan dengan metode Fuzzy Time Series Markov Chain. Namun, perlu diingat bahwa pemilihan model terbaik tidak hanya ditentukan oleh nilai error dan akurasi saja. Terdapat beberapa faktor lain yang perlu dipertimbangkan, seperti karakteristik data, kompleksitas model, dan interpretasi hasil peramalan.

COMPLETION OF THE DIFFUSION WAVE FLOOD TRACKING MODEL USING THE METHOD OF LINES (MOL)

2024-12-17T03:38:00+00:00

The flood tracking model is a method that can be used to predict when a flood will occur. The flood wave model is developed using a diffusion equation consisting of mass conservation equations and momentum conservation equations. This research was conducted to determine the application of the Method of Lines (MOL) in solving flood tracking models using the diffusion equation. The steps involved are discretizing the flood wave diffusion tracking equation by replacing the spatial derivative using the central difference method, resulting in a system of ordinary differential equations. Then, solving the system of ordinary differential equations using the fourth-order Runge Kutta method. The approach used in this research is quantitative. Simulations are performed by inputting a sample case and entering the data into the MATLAB program. The flow discharge produced increases as the flow velocity increases, and the resulting graph becomes more concave as the velocity increases. Thus, by knowing the changes in flow velocity, flow width, and flow depth in the upstream area of the river, it can be predicted how much the water discharge will change at each observation point downstream of the river.

HUBUNGAN ANTARA MATRIKS SIRKUIT DAN MATRIKS INSIDENSI DARI SUATU GRAF

2024-10-22T07:29:57+00:00

Meskipun penyajian graf dengan gambar yang terdiri dari titik dan busur memberikan cara yang sangat jelas secara visual, akan tetapi ada represantasi lain yang lebih baik untuk pemrosesan graf secara komputer yaitu menggunakan matriks. Selain memudahkan dalam manipulasi aljabar, aljabar matriks dapat dengan mudah diterapkan untuk mempelajari sifat-sifat struktural graf dari sudut pandang aljabar. di antaranya dalam aplikasi teori graf untuk analisis jaringan listrik dan riset operasi. Ada macam-macam representasi matriks dari suatu graf yaitu matriks adjasensi, matriks insidence, matriks sirkuit,, matriks cut-set, dan matriks path. Tulisan ini akan membahas tentang sifat-sifat matriks sirkuit, matriks insidensi dan sifat yang menghubungkan antara matriks sirkuit dan matriks insidensi graf.

Model Regresi Data Panel pada Faktor-Faktor yang Mempengaruhi Jumlah Kriminalitas Pencurian di Pulau Sumatera

2024-10-26T07:53:33+00:00

Sumatra island is the island with the highest theft rate in Indonesia. This study aims to determine the factors that have a significant effect on number of theft crime on the Sumatra Island from 2016 to 2021 by using panel data regression. This research uses panel data regression method which is a combination of cross section and time series data. The data used is secondary data obtained from Central Bureau of Statistics. Research variables include population density (X₁), average years of schooling (X₂), case completion rate (X₃), and number of drug abuse (X₄). The best model estimation was carried out for three models, including Common Effect Model (CEM), Fixed Effect Model (FEM), and Random Effect Model (REM). The selection of the best model of three models was carried out through the Chow test, Hausman test, and Lagrange Multiplier test. The best model result is individual effect FEM, with R² = 94.8%. After partial test, the variables that have significant effect on number of theft crime in Sumatera Island are X₂, X₃, X₄. The MAPE value of the best model is 23.15% which shows a feasible category.