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All Journal FARABI: Jurnal Matematika dan Pendidikan Matematika Research in the Mathematical and Natural Sciences Jurnal Riset Mahasiswa Matematika Limits: Journal of Mathematics and Its Applications
Nurwan
Universitas Negeri Gorontalo, Gorontalo-Indonesia
Computer Science & IT Decision Sciences, Operations Research & Management Education Mathematics

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Bifurkasi Periode Ganda dan Neimark-Sacker pada Model Diskret Leslie-Gower dengan Fungsi Respon Ratio-Dependent Reza Mokodompit; Nurwan; Emli Rahmi
Limits: Journal of Mathematics and Its Applications Vol. 17 No. 1 (2020): Limits: Journal of Mathematics and Its Applications Volume 17 Nomor 1 Edisi Ju
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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Abstract

Dinamika model Leslie-Gower dengan fungsi respon ratio-dependent yang didiskretisasi menggunakan skema Euler maju adalah fokus utama pada artikel ini. Analisis diawali dengan mengidentifikasi eksistensi dari titik ekuilibrium dan kestabilan lokalnya. Diperoleh empat titik ekuilibrium yaitu titik kepunahan kedua populasi dan titik kepunahan predator yang selalu tidak stabil, dan titik kepunahan prey dan eksistensi kedua populasi yang stabil kondisional. Selanjutnya dipelajari eksistensi dari bifurkasi periode ganda dan Neimark-Sacker di sekitar titik eksistensi kedua populasi sebagai akibat perubahan parameter h ( time-step ). Dari hasil analisis ditemukan bahwa bifurkasi periode ganda terjadi setelah melewati h=h_a atau h=h_c dan bifurkasi Neimark-Sacker terjadi setelah melewati h=hb. Di akhir pembahasan, diberikan simulasi numerik yang mendukung hasil analisis sebelumnya.
Sifat Fundamental Pada Granum Eulerian Suaib A. Siraj; Asriadi; Djihad Wungguli; Hasan S. Panigoro; Nurwan; Nisky I. Yahya
Limits: Journal of Mathematics and Its Applications Vol. 21 No. 2 (2024): Limits: Journal of Mathematics and Its Applications Volume 21 Nomor 2 Edisi Ju
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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Abstract

Mathematical analysis has several important connections with graph theory. Although initially, they may seem like two separate branches of mathematics, there are relationship between them in several aspects, such as graphs as mathematical objects that can be analyzed using concepts from analytic mathematics. In graph theory, one often studies distance, connectivity, and paths within a graph. These can be further analyzed using analytic mathematics, such as in the structure of natural numbers. Literature studies on graph theory, especially Eulerian graphs, are interesting to explore. An Eulerian path in a graph G is a path that includes every edge of graph G exactly once. An Eulerian path is called closed if it starts and ends at the same vertex. The concept of granum theory as a generalization of undirected graphs on number structures provides a rigorous approach to graph theory and demonstrates some fundamental properties of undirected graph generalization. The focus of this study is to introduce the connectivity properties of Eulerian granum. The granum G(e,M) is called connected if for every u,v E M with u != v there exists a path subgranumG^' (e,M^' )c G(e,M)  where u,v E M^' and is called an Eulerian granum if there exists a surjective mapping O: [||E(G(e,M))|| + 1]-> M such that e(o(n),o(n+1))=1 for every n E [||E(G(e,M))||]. This property provides a deeper understanding of the structure and characteristics of Eulerian granum, which have not been fully comprehended until now.
Model Aljabar Max-Plus pada Sistem Distribusi Produk Bakery dengan Representasi Petri Net Siti Nurlaila Mustapa; Nurwan Nurwan; La Ode Nashar
FARABI: Jurnal Matematika dan Pendidikan Matematika Vol 9 No 1 (2026): FARABI: Jurnal Matematika dan Pendidikan Matematika
Publisher : Program Studi Pendidikan Matematika FKIP UNIVA Medan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.47662/farabi.v9i1.1397

Abstract

Distribution efficiency is a critical aspect of bakery product distribution systems, as delivery delays affect product freshness, operational costs, and service reliability to customers. This study aims to develop a mathematical model to analyze product distribution time at UD. Win Win Bakery by integrating Petri Nets and Max-Plus Algebra. Petri Nets are used to represent the sequential, event-based distribution process, including vehicle preparation, goods loading, distribution travel, goods unloading, and the return trip to the factory. The Petri Net structure is then transformed into a Max-Plus Algebra model and matrix to calculate the total distribution time for each team. Data were collected through observations and interviews regarding distribution schedules, routes, number of vehicles, loading time, unloading time, and travel duration. The results show significant variations in distribution times among the nine delivery teams. The longest durations were found on the Toboli–Parigi, Ampibabo, and Kotamobagu routes, indicating workload imbalance and potential bottlenecks in the distribution system. The main contribution of this study lies in the application of Max-Plus Algebra supported by Petri Nets as a structured framework to identify time inefficiencies in regional-scale distribution. The implications of this study suggest that Max-Plus Algebra can be effectively used in discrete event-based distribution systems and supports route evaluation, workload balancing, and operational decision-making in perishable product logistics.
Determinan dan Invers Matriks Toeplitz Bentuk Khusus Ordo n×n Berpangkat Bilangan Bulat Positif Menggunakan Ekspansi Kofaktor Verawaty Moha; Nurwan Nurwan; Armayani Arsal
Jurnal Riset Mahasiswa Matematika Vol 5, No 5 (2026): Jurnal Riset Mahasiswa Matematika
Publisher : Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v5i5.43654

Abstract

Penelitian ini bertujuan untuk menentukan bentuk umum perpangkatan, determinan, dan invers matriks Toeplitz bentuk khusus berordo n×n berpangkat bilangan bulat positif menggunakan metode ekspansi kofaktor. Metode penelitian dilakukan secara analitik melalui studi literatur, dimulai dengan mengamati pola elemen hasil perpangkatan matriks berordo kecil, merumuskan bentuk umum, dan membuktikannya menggunakan metode induksi matematika. Hasil penelitian menunjukkan bahwa elemen-elemen diagonal atas matriks hasil perpangkatan membentuk pola koefisien binomial. Berdasarkan metode ekspansi kofaktor dan matriks adjoin, diperoleh formula umum determinan matriks Toeplitz khusus tersebut, yaitu \(\det(T_n^m) = a^{nm}\), serta formula umum invers yang dinyatakan secara eksplisit berdasarkan elemen-elemen matriksnya. Formula ini dapat digunakan untuk menyederhanakan perhitungan determinan dan invers matriks Toeplitz berpola khusus berordo besar tanpa memerlukan prosedur komputasi yang panjang.
Penjadwalan Mata Pelajaran Menggunakan Metode Integer Linear Programming di SMA Negeri 1 Tilango Fitria Djafar; Muhammad Rifai Katili; Salmun K Nasib; Nurwan Nurwan; Djihad Wungguli; Armayani Arsal
Research in the Mathematical and Natural Sciences Vol. 4 No. 1 (2025): November 2024-April 2025
Publisher : Scimadly Publishing

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.55657/rmns.v4i1.200

Abstract

Penjadwalan mata pelajaran secara optimal sangat penting untuk memastikan kelancaran kegiatan belajar dan mengajar. Di SMA Negeri 1 Tilango, penjadwalan yang dilakukan secara manual oleh pihak kurikulum cenderung memakan waktu yang cukup lama, sehingga sering terjadi bentrok antar mata pelajaran pada waktu yang bersamaan. Proses penjadwalan manual ini cukup sulit karena harus memenuhi semua aturan dan kebijakan sekolah yang berlaku. Untuk mengatasi tantangan tersebut, digunakan metode integer linear programming (ILP) yang dapat membantu menyusun jadwal mata pelajaran secara lebih efisien dan terstruktur. Penelitian ini bertujuan untuk menghasilkan jadwal mata pelajaran yang ideal dengan meminimalkan total bobot pelajaran, hari, dan waktu menggunakan metode ILP. Penyusunan jadwal diselesaikan dengan bantuan software Lingo 18.0. Hasil penelitian menunjukkan bahwa jadwal yang dihasilkan dengan metode ILP lebih optimal dibandingkan dengan penjadwalan manual, karena mampu memenuhi semua batasan dan kendala yang telah ditentukan oleh sekolah..
Pengelompokan Data Stunting di Indonesia Menggunakan Metode X-Means dan Agglomerative Hierarchical Clustering Nur Dhea Wahab; Salmun K. Nasib; Nurwan; Djihad Wungguli; Nisky Imansyah Yahya
Research in the Mathematical and Natural Sciences Vol. 4 No. 1 (2025): November 2024-April 2025
Publisher : Scimadly Publishing

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.55657/rmns.v4i1.201

Abstract

Stunting is one of the serious problems that threaten the quality of human resources in Indonesia. This study aims to analyze the patterns and characteristics of stunting in Indonesia by applying the X-Means clustering method and Agglomerative Hierarchical Clustering (AHC). The X-Means method is used to determine the optimal number of clusters automatically by utilizing the Bayesian Information Criterion (BIC), while AHC forms a dendrogram to understand the multilevel structure of the clusters formed. Based on the analysis, the X-Means method produces three optimal clusters with the smallest BIC value of 651.9475, where cluster 1 consists of 17 provinces, cluster 2 includes 12 provinces, and cluster 3 includes 5 provinces. The AHC method with the Single Linkage approach also produced three optimal clusters, with cluster 1 covering 32 provinces, cluster 2 consisting of 1 province (West Nusa Tenggara), and cluster 3 covering 1 province (East Nusa Tenggara), as well as the highest Silhouette Index value of 0.28. The results show that both methods provide a comprehensive picture of stunting patterns in Indonesia, which can be used as a basis for designing more targeted intervention programs according to the characteristics of each cluster. This data-driven strategy is expected to increase policy effectiveness in reducing stunting in Indonesia.
Co-Authors Armayani Arsal Asriadi Djihad Wungguli Fitria Djafar Hasan S. Panigoro La Ode Nashar Muhammad Rifai Katili Nisky I. Yahya Nisky Imansyah Yahya Nur Dhea Wahab Rahmi, Emli Reza Mokodompit Salmun K. Nasib Siti Nurlaila Mustapa Suaib A. Siraj Verawaty Moha